Natural gas having a molar analysis of 60% methane (CH4)

The analysis on a mass basis of an ideal gas mixture at \(50^{\circ} \mathrm{F}\), \(25 \mathrm{lbf} / \mathrm{in}^{2}\) is 60% \(\mathrm{CO}_{2}\), 25% \(\mathrm{SO}_{2}), and 15% \(\mathrm{N}_{2}\). Determine (a) the analysis in terms of mole fractions. (b) the apparent molecular weight of the mixture. (c) the partial pressure of each component, in \(\mathrm{lbf} / \mathrm{in}^{2}\) (d) the volume occupied by 20 lb of the mixture, in \(\mathrm{ft}^{3}\).

The molar analysis of a gas mixture at \(30^{\circ} \mathrm{C}\), 2 bar is 40% \(\mathrm{N}_{2}\), 50% \(\mathrm{CO}_{2}\), and 10% \(\mathrm{CH}_{4}\). Determine (a) the analysis in terms of mass fractions. (b) the partial pressure of each component, in bar. (c) the volume occupied by 10 kg of mixture, in m3.

The analysis on a molar basis of a gas mixture at \(50^{\circ} \mathrm{F}\), 1 atm is 20% Ar, 35% \(\mathrm{CO}_{2}\), and 45% \(\mathrm{O}_{2}\). Determine (a) the analysis in terms of mass fractions. (b) the partial pressure of each component, in \(\mathrm{lbf} / \mathrm{in}^{2}\) (c) the volume occupied by 10 lb of mixture, in \(\mathrm{ft}^{3}\).

The analysis on a mass basis of a gas mixture at \(40^{\circ} \mathrm{F}\), \(14.7 \mathrm{lbf} / \mathrm{in}^{2}\) is 60% \9\mathrm{CO}_{2}\), 25% CO, 15% \(\mathrm{O}_{2}\). Determine (a) the analysis in terms of mole fractions. (b) the partial pressure of each component, in \(\mathrm{lbf} / \mathrm{in}^{2}\) (c) the volume occupied by 10 lb of the mixture, in \(\mathrm{ft}^{3}\).

The analysis on a mass basis of an ideal gas mixture at \(30^{\circ} \mathrm{F}\), \(15 \mathrm{lbf} / \mathrm{in}^{2}\) is 55% \(\mathrm{CO}_{2}\), 30% CO, 15% \(\mathrm{O}_{2}\). Determine (a) the analysis in terms of mole fractions. (b) the apparent molecular weight of the mixture. (b) the partial pressure of each component, in \(\mathrm{lbf} / \mathrm{in}^{2}\) (c) the volume occupied by 10 lb of the mixture, in \(\mathrm{ft}^{3}\).

A 4-lb mass of oxygen (\(\mathrm{O}_{2}\)) is mixed with 8 lb of another gas to form a mixture that occupies \(45 \mathrm{ft}^{3}\) at \(150^{\circ} \mathrm{F}\), \(40 \mathrm{lbf} / \mathrm{in}^{2}\) Applying ideal gas mixture principles, determine (a) the molecular weight of the unspecified gas. (b) the analysis of the mixture in terms of mole fractions.

A vessel having a volume of \(0.28 \mathrm{m}^{3}\) contains a mixture at \(40^{\circ} \mathrm{C}\), 6.9 bar with a molar analysis of 70% \(\mathrm{O}_{2}\), 30% \(\mathrm{CH}_{4}\). Determine the mass of methane that would have to be added and the mass of oxygen that would have to be removed, each in kg, to obtain a mixture having a molar analysis of 30% \(\mathrm{O}_{2}\), 70% \(\mathrm{CH}_{4}\) at the same temperature and pressure.

Nitrogen (\(\mathrm{N}_{2}\)) at 150 kPa, \(40^{\circ} \mathrm{C}\) occupies a closed, rigid container having a volume of 1 m3. If 2 kg of oxygen (\(\mathrm{O}_{2}\)) is added to the container, what is the molar analysis of the resulting mixture? If the temperature remains constant, what is the pressure of the mixture, in kPa?

A flue gas in which the mole fraction of \(\mathrm{SO}_{2}\) is 0.002 enters a packed bed wet scrubber operating at steady state at \(200^{\circ} \mathrm{F}\), 1 atm with a volumetric flow rate of \(35,000 \mathrm{ft}^{3} / \mathrm{h}\). If the scrubber removes 90% (molar basis) of the entering SO2, determine the rate at which \(\mathrm{SO}_{2}\) is removed, in lb/h.

A gas mixture with a molar analysis of 20% \(\mathrm{C}_{3} \mathrm{H}_{8}\) (propane) and 80% air enters a control volume operating at steady state at location 1 with a mass flow rate of 5 kg/min, as shown in Fig. P12.10. Air enters as a separate stream at 2 and dilutes the mixture. A single stream exits with a mole fraction of propane of 3%. Assuming air has a molar analysis of 21% \(\mathrm{O}_{2}\) and 79% \(\mathrm{N}_{2}\), determine (a) the molar flow rate of the entering air at 2, in kmol/min. (b) the mass flow rate of oxygen in the exiting stream, in kg/min.

A gas mixture in a piston–cylinder assembly consists of 2 lb of \(\mathrm{N}_{2}\) and 3 lb of He. Determine (a) the composition in terms of mass fractions. (b) the composition in terms of mole fractions. (c) the heat transfer, in Btu, required to increase the mixture temperature from 70 to \(150^{\circ} \mathrm{F}\), while keeping the pressure constant. (d) the change in entropy of the mixture for the process of part (c), in \(\mathrm{Btu} /{ }^{\circ} \mathrm{R}\).

Two kg of a mixture having an analysis on a mass basis of 30% \(\mathrm{N}_{2}\), 40% \(\mathrm{CO}_{2}\), 30% \(\mathrm{O}_{2}\) is compressed adiabatically from 1 bar, 300 K to 4 bar, 500 K. Determine (a) the work, in kJ. (b) the amount of entropy produced, in kJ/K.

As illustrated in Fig. P12.13, an ideal gas mixture in a piston–cylinder assembly has a molar analysis of 30% carbon dioxide (\(\mathrm{CO}_{2}\)) and 70% nitrogen (\(\mathrm{N}_{2}\)). The mixture is cooled at constant pressure from 425 to 325 K. Assuming constant specific heats evaluated at 375 K, determine the heat transfer and the work, each in kJ per kg of mixture.

A closed, rigid tank having a volume of \(0.1 \mathrm{m}^{3}\) contains 0.7 kg of N2 and 1.1 kg of \(\mathrm{CO}_{2}\) at \(27^{\circ} \mathrm{C}\). Determine (a) the analysis of the mixture in terms of mass fractions. (b) the analysis of the mixture in terms of mole fractions. (c) the partial pressure of each component, in bar. (d) the mixture pressure, in bar. (e) the heat transfer, in kJ, required to bring the mixture to \(127^{\circ} \mathrm{C}\). (f) the entropy change of the mixture for the process of part (e) in kJ/K.

A mixture consisting of 2.8 kg of \(\mathrm{N}_{2}\) and 3.2 kg of \(\mathrm{O}_{2}\) is compressed from 1 bar, 300 K to 2 bar, 600 K. During the process there is heat transfer from the mixture to the surroundings, which are at \(27^{\circ} \mathrm{C}\). The work done on the mixture is claimed to be 2300 kJ. Can this value be correct?

A mixture having a molar analysis of 50% \(\mathrm{CO}_{2}\), 33.3% CO, and 16.7% \(\mathrm{O}_{2}\) enters a compressor operating at steady state at \(37^{\circ} \mathrm{C}\), 1 bar, 40 m/s with a mass flow rate of 1 kg/s and exits at \(237^{\circ} \mathrm{C}\), 30 m/s. The rate of heat transfer from the compressor to its surroundings is 5% of the power input. (a) Neglecting potential energy effects, determine the power input to the compressor, in kW. (b) If the compression is polytropic, evaluate the polytropic exponent n and the exit pressure, in bar.

A mixture of 5 kg of \(\mathrm{H}_{2}\) and 4 kg of \(\mathrm{O}_{2}\) is compressed in a piston–cylinder assembly in a polytropic process for which n = 1.6. The temperature increases from 40 to \(250^{\circ} \mathrm{C}\). Using constant values for the specific heats, determine (a) the heat transfer, in kJ. (b) the entropy change, in kJ/K.

A gas turbine receives a mixture having the following molar analysis: 10% \9\mathrm{CO}_{2}\), 19% \(\mathrm{H}_{2} \mathrm{O}\), 71% \(\mathrm{N}_{2}\) at 720 K, 0.35 MPa and a volumetric flow rate of 3.2 m3/s. The mixture exits the turbine at 380 K, 0.11 MPa. For adiabatic operation with negligible kinetic and potential energy effects, determine the power developed at steady state, in kW.

A gas mixture at 1500 K with the molar analysis 10% \(\mathrm{CO}_{2}\), 20% \(\mathrm{H}_{2} \mathrm{O}\), 70% \(\mathrm{N}_{2}\) enters a waste-heat boiler operating at steady state, and exits the boiler at 600 K. A separate stream of saturated liquid water enters at 25 bar and exits as saturated vapor with a negligible pressure drop. Ignoring stray heat transfer and kinetic and potential energy changes, determine the mass flow rate of the exiting saturated vapor, in kg per kmol of gas mixture.

Two cubic feet of gas A initially at \(60^{\circ} \mathrm{F}\), \(15 \mathrm{lbf} / \mathrm{in}^{2}\) is allowed to mix adiabatically with \(8 \mathrm{ft}^{3}\) of gas B initially at \(60^{\circ} \mathrm{F}\), \(5 \mathrm{lbf} / \mathrm{in}^{2}\) Assuming that the total volume remains constant and applying ideal gas mixture principles, determine (a) the final mixture pressure, in \(\mathrm{lbf} / \mathrm{in}^{2}\) (b) the entropy change of each gas in \(\mathrm{Btu} / \mathrm{lbmol} \cdot{ }^{\circ} \mathrm{R}\).

An equimolar mixture of helium (He) and carbon dioxide (\(\mathrm{CO}_{2}\)) enters an insulated nozzle at \(260^{\circ} \mathrm{F}\), 5 atm, 100 ft/s and expands isentropically to a velocity of 1110 ft/s. Determine the temperature, in \({ }^{\circ} \mathrm{F}\), and the pressure, in atm, at the nozzle exit. Neglect potential energy effects.

A gas mixture having a molar analysis of 60% \(\mathrm{O}_{2}\) and 40% \(\mathrm{N}_{2}\) enters an insulated compressor operating at steady state at 1 bar, \(20^{\circ} \mathrm{C}\) with a mass flow rate of 0.5 kg/s and is compressed to 5.4 bar. Kinetic and potential energy effects are negligible. For an isentropic compressor efficiency of 78%, determine (a) the temperature at the exit, in \({ }^{\circ} \mathrm{C}\). (b) the power required, in kW. (c) the rate of entropy production, in kW/K.

A mixture having a molar analysis of 60% \(\mathrm{N}_{2}\), 17% \(\mathrm{CO}_{2}\), and 17% \(\mathrm{H}_{2} \mathrm{O}\) enters a turbine at 1000 K, 8 bar, with a mass flow rate of 2 kg/s and expands isentropically to a pressure of 1 bar. Ignoring kinetic and potential energy effects, determine for steady-state operation (a) the temperature at the exit, in K. (b) the power developed by the turbine, in kW.

A mixture having a molar analysis of 60% \(\mathrm{N}_{2}\) and 40% \(\mathrm{CO}_{2}\) enters an insulated compressor operating at steady state at 1 bar, \(30^{\circ} \mathrm{C}\) with a mass flow rate of 1 kg/s and is compressed to 3 bar, \(147^{\circ} \mathrm{C}\). Neglecting kinetic and potential energy effects, determine (a) the power required, in kW. (b) the isentropic compressor efficiency. (c) the rate of exergy destruction, in kW, for \(T_{0}=300 \mathrm{~K}\).

An equimolar mixture of \(\mathrm{N}_{2}\) and \(\mathrm{CO}_{2}\) enters a heat exchanger at \(-40^{\circ} \mathrm{F}\), \(500 \mathrm{lbf} / \mathrm{in}^{2}\) and exits at \(500^{\circ} \mathrm{F}\), \(500 \mathrm{lbf} / \mathrm{in}^{2}\) The heat exchanger operates at steady state, and kinetic and potential energy effects are negligible. (a) Using the ideal gas mixture concepts of the present chapter, determine the rate of heat transfer to the mixture, in Btu per lbmol of mixture flowing. (b) Compare with the value of the heat transfer determined using the generalized enthalpy chart (Fig. A-4), together with Kay’s rule (see Sec. 11.8).

Natural gas having a molar analysis of 60% methane \(\left(\mathrm{CH}_{4}\right)\) and 40% ethane \(\left(\mathrm{C}_{2} \mathrm{H}_{6}\right)\) enters a compressor at 340 K, 6 bar and is compressed isothermally without internal irreversibilities to 20 bar. The compressor operates at steady state, and kinetic and potential energy effects are negligible. (a) Assuming ideal gas behavior, determine for the compressor the work and heat transfer, each in kJ per kmol of mixture flowing. (b) Compare with the values for work and heat transfer, respectively, determined assuming ideal solution behavior (Sec. 11.9.5). For the pure components at 340 K:

An insulated tank having a total volume of \(0.6 \mathrm{~m}^{3}\) is divided into two compartments. Initially one compartment contains \(0.4 \mathrm{~m}^{3}\) of hydrogen \(\left(\mathrm{H}_{2}\right) \text { at } 127^{\circ} \mathrm{C} \text {, }\), 2 bar and the other contains nitrogen \(\left(\mathrm{N}_{2}\right) \text { at } 27^{\circ} \mathrm{C}\), 4 bar. The gases are allowed to mix until an equilibrium state is attained. Assuming the ideal gas model with constant specific heats, determine (a) the final temperature, in \({ }^{\circ} \mathrm{C}\). (b) the final pressure, in bar. (c) the amount of entropy produced, in kJ/K.

Using the ideal gas model with constant specific heats, determine the mixture temperature, in K, for each of two cases: (a) Initially, 0.6 kmol of \(\mathrm{O}_{2}\) at 500 K is separated by a partition from 0.4 kmol of \(\mathrm{H}_{2}\) at 300 K in a rigid insulated vessel. The partition is removed and the gases mix to obtain a final equilibrium state. (b) Oxygen (\(\mathrm{O}_{2}\)) at 500 K and a molar flow rate of 0.6 kmol/s enters an insulated control volume operating at steady state and mixes with \(\mathrm{H}_{2}\) entering as a separate stream at 300 K and a molar flow rate of 0.4 kmol/s. A single mixed stream exits. Kinetic and potential energy effects can be ignored.

A system consists initially of \(n_{\mathrm{A}}\) moles of gas A at pressure p and temperature T and \(n_{\mathrm{B}}\) moles of gas B separate from gas A but at the same pressure and temperature. The gases are allowed to mix with no heat or work interactions with the surroundings. The final equilibrium pressure and temperature are p and T, respectively, and the mixing occurs with no change in total volume. (a) Assuming ideal gas behavior, obtain an expression for the entropy produced in terms of \(\bar{R}, n_{\mathrm{A}}, \text { and } n_{\mathrm{B}}\). (b) Using the result of part (a), demonstrate that the entropy produced has a positive value. (c) Would entropy be produced when samples of the same gas at the same temperature and pressure mix? Explain.

Carbon dioxide \(\left(\mathrm{CO}_{2}\right)\) at \(197^{\circ} \mathrm{C}\), 2 bar enters a chamber at steady state with a molar flow rate of 2 kmol/s and mixes with nitrogen \(\left(\mathrm{N}_{2}\right)\) entering at \(2\7^{\circ} \mathrm{C}\), 2 bar with a molar flow rate of 1 kmol/s. Heat transfer from the mixing chamber occurs at an average surface temperature of \(127^{\circ} \mathrm{C}\). A single stream exits the mixing chamber at \(127^{\circ} \mathrm{C}\), 2 bar and passes through a duct, where it cools at constant pressure to \(42^{\circ} \mathrm{C}\) through heat transfer with the surroundings at \(27^{\circ} \mathrm{C}\). Kinetic and potential energy effects can be ignored. Determine the rates of heat transfer and exergy destruction, each in kW, for control volumes enclosing (a) the mixing chamber only. (b) the mixing chamber and enough of the nearby surroundings that heat transfer occurs at \(27^{\circ} \mathrm{C}\). (c) the duct and enough of the nearby surroundings that heat transfer occurs at \(27^{\circ} \mathrm{C}\). Let \(T_{0}=27^{\circ} \mathrm{C}\).

Two kg of \(\mathrm{N}_{2}\) at 450 K, 7 bar is contained in a rigid tank connected by a valve to another rigid tank holding 1 kg of \(\mathrm{O}_{2}\) at 300 K, 3 bar. The valve is opened and gases are allowed to mix, achieving an equilibrium state at 370 K. Determine (a) the volume of each tank, in \(m_{3}\). (b) the final pressure, in bar. (c) the heat transfer to or from the gases during the process, in kJ. (d) the entropy change of each gas, in kJ/K.

An insulated tank having a total volume of \(60 \mathrm{ft}^{3}\) is divided into two compartments. Initially one compartment having a volume of \(20 \mathrm{ft}^{3}\) contains 4 lb of carbon monoxide (CO) at \(500^{\circ} \mathrm{F}\) and the other contains 0.8 lb of helium (He) at \(60^{\circ} \mathrm{F}\). The gases are allowed to mix until an equilibrium state is attained. Determine (a) the final temperature, in \({ }^{\circ} \mathrm{F}\). (b) the final pressure, in \(\text { lbf/in.2 }\) (c) the exergy destruction, in Btu, for \(T_{0}=60^{\circ} \mathrm{F}\).

A rigid insulated tank has two compartments. Initially one compartment is filled with 2.0 lbmol of argon at \(150^{\circ} \mathrm{F}\), \(50 \mathrm{lbf} / \mathrm{in}^{2}\) and the other is filled with 0.7 lbmol of helium at \(0^{\circ} \mathrm{F}\), \(15 \mathrm{lbf} / \mathrm{in}^{2}\) The gases are allowed to mix until an equilibrium state is attained. Determine (a) the final temperature, in \({ }^{\circ} \mathrm{C}\). (b) the final pressure, in atm. (c) the amount of entropy produced, in \(\mathrm{Btu} /{ }^{\circ} \mathrm{R}\).

A device is being designed to separate a natural gas having a molar analysis of 94% \(\mathrm{CH}_{4\) and 6% \(\mathrm{C}_{2} \mathrm{H}_{6}\) into components. The device will receive natural gas at 208C, 1 atm with a volumetric flow rate of \(100 \mathrm{m}^{3} / \mathrm{s}\). Separate streams of \(\mathrm{CH}_{4}\) and \(\mathrm{C}_{2} \mathrm{H}_{6}\) will exit, each at \(20^{\circ} \mathrm{C}\), 1 atm. The device will operate isothermally at \(20^{\circ} \mathrm{C}\). Ignoring kinetic and potential energy effects and assuming ideal gas behavior, determine the minimum theoretical work input required at steady state, in kW.

Air at \(50^{\circ} \mathrm{C}\), 1 atm and a volumetric flow rate of \(60 \mathrm{~m}^{3} / \mathrm{min}\) enters an insulated control volume operating at steady state and mixes with helium entering as a separate stream at \(120^{\circ} \mathrm{C}\), 1 atm and a volumetric flow rate of \(25 \mathrm{~m}^{3} / \mathrm{min}\). A single mixed stream exits at 1 atm. Ignoring kinetic and potential energy effects, determine for the control volume (a) the temperature of the exiting mixture, in \({ }^{\circ} \mathrm{C}\). (b) the rate of entropy production, in kW/K. (c) the rate of exergy destruction, in kW, for \(T_{0}=295 \mathrm{K}\).

Argon (Ar), at 300 K, 1 bar with a mass flow rate of 1 kg/s enters the insulated mixing chamber shown in Fig. P12.36 and mixes with carbon dioxide \(\left(\mathrm{CO}_{2}\right)\) entering as a separate stream at 575 K, 1 bar with a mass flow rate of 0.5 kg/s. The mixture exits at 1 bar. Assume ideal gas behavior with k 5 1.67 for Ar and k 5 1.25 for \(\mathrm{CO}_{2}\). For steady-state operation, determine (a) the molar analysis of the exiting mixture. (b) the temperature of the exiting mixture, in K. (c) the rate of entropy production, in kW/K.

Carbon dioxide (\(\mathrm{CO}_{2}\)) at \(100^{\circ} \mathrm{F}\), \(18 \mathrm{lbf} / \mathrm{in}^{2}\) and a volumetric flow rate of \(250 \mathrm{ft}^{3} / \mathrm{min}\) enters an insulated control volume operating at steady state and mixes with oxygen (\(\mathrm{O}_{2}\)) entering as a separate stream at \(190^{\circ} \mathrm{F}\), 18 lbf/ in.2 and a mass flow rate of 60 lb/min. A single mixed stream exits at \(15 \mathrm{lbf} / \mathrm{in}^{2}\) Kinetic and potential energy effects can be ignored. Using the ideal gas model with constant specific heats, determine for the control volume (a) the temperature of the exiting mixture, in \({ }^{\circ} \mathrm{F}\). (b) the rate of entropy production, in \(\text { Btu } / \min \cdot{ }^{\circ} \mathrm{R}\). (c) the rate of exergy destruction, in Btu/min, for \(T_{0}=40^{\circ} \mathrm{F}\).

Air at \(77^{\circ} \mathrm{C}\), 1 bar, and a molar flow rate of 0.1 kmol/s enters an insulated mixing chamber operating at steady state and mixes with water vapor entering at \(277^{\circ} \mathrm{C}\), 1 bar and a molar flow rate of 0.3 kmol/s. The mixture exits at 1 bar. Kinetic and potential energy effects can be ignored. For the chamber, determine (a) the temperature of the exiting mixture, in \({ }^{\circ} \mathrm{C}\). (b) the rate of entropy production, in kW/K.

A gas mixture required in an industrial process is prepared by first allowing carbon monoxide (CO) at \(80^{\circ} \mathrm{F}\), \(18 \mathrm{lbf} / \mathrm{in}^{2}\) to enter an insulated mixing chamber operating at steady state and mix with argon (Ar) entering at \(380^{\circ} \mathrm{F}\), \(18 \mathrm{lbf} / \mathrm{in}^{2}\) The mixture exits the chamber at \(140^{\circ} \mathrm{F}\), \(16 \mathrm{lbf} / \mathrm{in}^{2}\) and is then allowed to expand in a throttling process through a valve to \(14.7 \mathrm{lbf} / \mathrm{in}^{2}\) Determine (a) the mass and molar analyses of the mixture. (b) the temperature of the mixture at the exit of the valve, in \({ }^{\circ} \mathrm{F}\). (c) the rates of exergy destruction for the mixing chamber and the valve, each in Btu per lb of mixture, for \(T_{0}=40^{\circ} \mathrm{F}\). Kinetic and potential energy effects can be ignored.

Helium at 400 K, 1 bar enters an insulated mixing chamber operating at steady state, where it mixes with argon entering at 300 K, 1 bar. The mixture exits at a pressure of 1 bar. If the argon mass flow rate is x times that of helium, plot versus x (a) the exit temperature, in K. (b) the rate of exergy destruction within the chamber, in kJ per kg of helium entering. Kinetic and potential energy effects can be ignored. Let \(T_{0}=300 \mathrm{K}\).

Hydrogen (\(\mathrm{H}_{2}\)) at \(77^{\circ} \mathrm{C}\), 4 bar enters an insulated chamber at steady state, where it mixes with nitrogen (\(\mathrm{N}_{2}\)) entering as a separate stream at \(277^{\circ} \mathrm{C}\), 4 bar. The mixture exits at 3.8 bar with the molar analysis 75% \(\mathrm{H}_{2}\), 25% \(\mathrm{N}_{2}\). Kinetic and potential energy effects can be ignored. Determine (a) the temperature of the exiting mixture, in \({ }^{\circ} \mathrm{C}\). (b) the rate at which entropy is produced, in kJ/K per kmol of mixture exiting.

An insulated, rigid tank initially contains 1 kmol of argon (Ar) at 300 K, 1 bar. The tank is connected by a valve to a large vessel containing nitrogen (\(\(\mathrm{N}_{2}\)) at 500 K, 4 bar. A quantity of nitrogen flows into the tank, forming an argon–nitrogen mixture at temperature T and pressure p. Plot T, in K, and p, in bar, versus the amount of \(\mathrm{N}_{2}\) within the tank, in kmol.

A stream of oxygen (\(\mathrm{O}_{2}\)) at \(100^{\circ} \mathrm{F}\), 2 atm enters an insulated chamber at steady state with a mass flow rate of 1 lb/min and mixes with a stream of air entering separately at \(200^{\circ} \mathrm{F}\), 1.5 atm with a mass flow rate of 2 lb/min. The mixture exits at a pressure of 1 atm. Kinetic and potential energy effects can be ignored. On the basis of constant specific heats, determine (a) the temperature of the exiting mixture, in \({ }^{\circ} \mathrm{F}\). (b) the rate of exergy destruction, in Btu/min, for \(T_{0}=40^{\circ} \mathrm{F}\).

A device is being designed to separate into components a natural gas consisting of \(\mathrm{CH}_{4}\) and \(\mathrm{C}_{2} \mathrm{H}_{6}\) in which the mole fraction of \(\mathrm{C}_{2} \mathrm{H}_{6}\), denoted by y, may vary from 0.05 to 0.50. The device will receive natural gas at \(20^{\circ} \mathrm{C}\), 1 atm with a volumetric flow rate of \(100 \mathrm{m}^{3} / \mathrm{s}\). Separate streams of \(\mathrm{CH}_{4}\) and \(\mathrm{C}_{2} \mathrm{H}_{6}\) will exit, each at \(20^{\circ} \mathrm{C}\), 1 atm. Heat transfer between the device and its surroundings occurs at \(20^{\circ} \mathrm{C}\). Ignoring kinetic and potential energy effects, plot versus y the minimum theoretical work input required at steady state, in kW.

A water pipe at \(5^{\circ} \mathrm{C}\) runs above ground between two buildings. The surrounding air is at \(35^{\circ} \mathrm{C}\). What is the maximum relative humidity the air can have before condensation occurs on the pipe?

The inside temperature of a wall in a dwelling is \(16^{\circ} \mathrm{C}\). If the air in the room is at \(21^{\circ} \mathrm{C}\), what is the maximum relative humidity the air can have before condensation occurs on the wall?

lecture hall having a volume of \(10^{6} \mathrm{ft}^{3}\) contains air at \(80^{\circ} \mathrm{F}\), 1 atm, and a humidity ratio of 0.01 lb of water vapor per lb of dry air. Using the appropriate equations, determine (a) the relative humidity. (b) the dew point temperature, in \({ }^{\circ} \mathrm{F}\). (c) the mass of water vapor contained in the room, in lb.

A large room contains moist air at \(30^{\circ} \mathrm{C}\), 102 kPa. The partial pressure of water vapor is 1.5 kPa. Determine (a) the relative humidity. (b) the humidity ratio, in kg(vapor) per kg(dry air). (c) the dew point temperature, in \({ }^{\circ} \mathrm{C}\). (d) the mass of dry air, in kg, if the mass of water vapor is 10 kg.

To what temperature, in \({ }^{\circ} \mathrm{C}\), must moist air with a humidity ratio of \(5 \times 10^{-3}\)(vapor) per kg(dry air) be cooled at a constant pressure of 2 bar to become saturated moist air?

A fixed amount of air initially at \(14.5 \mathrm{lbf} / \mathrm{in}^{2}, 80^{\circ} \mathrm{F}\), and a relative humidity of 50% is compressed isothermally until condensation of water begins. Determine the pressure of the mixture at the onset of condensation, in \(\mathrm{lbf} / \mathrm{in}^{2}\)

As shown in Fig. P12.51, moist air at \(30^{\circ} \mathrm{C}\), 2 bar, and 50% relative humidity enters a heat exchanger operating at steady state with a mass flow rate of 600 kg/h and is cooled at constant pressure to \(20^{\circ} \mathrm{C}\). Ignoring kinetic and potential energy effects, determine the rate of heat transfer from the moist air stream, in kJ/h.

Two pounds of moist air initially at \(100^{\circ} \mathrm{F}\), 1 atm, 40% relative humidity is compressed isothermally to 4 atm. If condensation occurs, determine the amount of water condensed, in lb. If there is no condensation, determine the final relative humidity.

A closed, rigid tank having a volume of \(3 \mathrm{m}^{3}\) contains moist air in equilibrium with liquid water at \(80^{\circ} \mathrm{C}\). The respective masses present initially are 10.4 kg of dry air, 0.88 kg of water vapor, and 0.17 kg of liquid water. If the tank contents are heated to \(160^{\circ} \mathrm{C}\), determine (a) the final pressure, in bar. (b) the heat transfer, in kJ.

Air at \(12^{\circ} \mathrm{C}\), 1 atm, and 40% relative humidity enters a heat exchanger with a volumetric flow rate of \(1 \mathrm{m}^{3} / \mathrm{s}\). A separate stream of dry air enters at \(280^{\circ} \mathrm{C}\), 1 atm with a mass flow rate of 0.875 kg/s and exits at \(220^{\circ} \mathrm{C}\). Neglecting heat transfer between the heat exchanger and its surroundings, pressure drops of each stream, and kinetic and potential energy effects, determine (a) the temperature of the exiting moist air, in \({ }^{\circ} \mathrm{C}\). (b) the rate of exergy destruction, in kW, for \(T_{0}=-12^{\circ} \mathrm{C}\).

Solve Problem 12.47 using the psychrometric chart, Fig. A-9E.

A mixture of nitrogen and water vapor at \(200^{\circ} \mathrm{F}\), 1 atm has the molar analysis 80% \(\mathrm{N}_{2}\), 20% water vapor. If the mixture is cooled at constant pressure, determine the temperature, in \({ }^{\circ} \mathrm{F}\), at which water vapor begins to condense.

A system consisting initially of \(0.5 \mathrm{~m}^{3}\) of air at \(35^{\circ} \mathrm{C}\), 1 bar, and 70% relative humidity is cooled at constant pressure to \(29^{\circ} \mathrm{C}\). Determine the work and heat transfer for the process, each in kJ.

Moist air initially at \(125^{\circ} \mathrm{C}\), 4 bar, and 50% relative humidity is contained in a \(2.5-\mathrm{m}^{3}\) closed, rigid tank. The tank contents are cooled. Determine the heat transfer, in kJ, if the final temperature in the tank is (a) \(110^{\circ} \mathrm{C}\), (b) \(30^{\circ} \mathrm{C}\).

A closed, rigid tank initially contains \(0.5 \mathrm{m}^{3}\) of moist air in equilibrium with \(0.1 \mathrm{m}^{3}\) of liquid water at \(80^{\circ} \mathrm{C}\) and 0.1 MPa. If the tank contents are heated to \(200^{\circ} \mathrm{C}\), determine (a) the final pressure, in MPa. (b) the heat transfer, in kJ.

Air at \(30^{\circ} \mathrm{C}\), 1.05 bar, and 80% relative humidity enters a dehumidifier operating at steady state. Moist air exits at \(15^{\circ} \mathrm{C}\), 1 bar, and 95% relative humidity. Condensate exits in a separate stream at \(15^{\circ} \mathrm{C}\). A refrigerant flows through the cooling coil of the dehumidifier with an increase in its specific enthalpy of 100 kJ per kg of refrigerant flowing. Heat transfer between the humidifier and its surroundings and kinetic and potential energy effects can be ignored. Determine the refrigerant flow rate, in kg per kg of dry air.

Gaseous combustion products with the molar analysis of 15% \(\mathrm{CO}_{2}\), 25% \(\mathrm{H}_{2} \mathrm{O}\), 60% \(\mathrm{n}_{2}\) enter an engine’s exhaust pipe at \(1100^{\circ} \mathrm{f}\), 1 atm and are cooled as they pass through the pipe, to \(125^{\circ} \mathrm{C}\), 1 atm. Determine the heat transfer at steady state, in Btu per lb of entering mixture.

Air at \(60^{\circ} \mathrm{F}\), \(14.7 \mathrm{lbf} / \mathrm{in}^{2}\), and 75% relative humidity enters an insulated compressor operating at steady state and is compressed to \(100 \mathrm{lbf} / \mathrm{in}^{2}\) The isentropic compressor efficiency is \(\eta_{\mathrm{c}}\). (a) For \(\eta_{\mathrm{c}}=0.8\), determine the temperature, in \({ }^{\circ} \mathrm{R}\), of the exiting air, and the work input required and the exergy destruction, each in Btu per lb of dry air flowing. Let \(T_{0}=520^{\circ} \mathrm{R}\). (b) Plot each of the quantities determined in part (a) versus \(\eta_{\mathrm{c}}\) ranging from 0.7 to 1.0.

Dry air enters a device operating at steady state at \(27^{\circ} \mathrm{C}\), 2 bar with a volumetric flow rate of \(300 \mathrm{m}^{3} / \mathrm{min}\). Liquid water is injected and a moist air stream exits at \(15^{\circ} \mathrm{C}\), 2 bar, and 91% relative humidity. Determine (a) the mass flow rate at the exit, in kg/min. (b) the temperature, in \({ }^{\circ} \mathrm{C}\), of the liquid water injected into the air stream. Ignore heat transfer between the device and its surroundings and neglect kinetic and potential energy effects.

A closed, rigid tank having a volume of \(1 \mathrm{m}^{3}\) contains a mixture of carbon dioxide (\(\mathrm{CO}_{2}\)) and water vapor at \(75^{\circ} \mathrm{C}\). The respective masses are 12.3 kg of carbon dioxide and 0.05 kg of water vapor. If the tank contents are cooled to \(20^{\circ} \mathrm{C}\), determine the heat transfer, in kJ, assuming ideal gas behavior.

At steady state, moist air at \(29^{\circ} \mathrm{C}\), 1 bar, and 50% relative humidity enters a device with a volumetric flow rate of \(13 \mathrm{m}^{3} / \mathrm{s}\). Liquid water at \(40^{\circ} \mathrm{C}\) is sprayed into the moist air with a mass flow rate of 22 kg/s. The liquid water that does not evaporate into the moist air stream is drained and flows to another device at \(26^{\circ} \mathrm{C}\) with a mass flow rate of 21.55 kg/s. A single moist air stream exits at 1 bar. Determine the temperature and relative humidity of the moist air stream exiting. Ignore heat transfer between the device and its surroundings and kinetic and potential energy effects.

Air enters a compressor operating at steady state at \(50^{\circ} \mathrm{C}\), 0.9 bar, 70% relative humidity with a volumetric flow rate of \(0.8 \mathrm{~m}^{3} / \mathrm{s}\). The moist air exits the compressor at \(195^{\circ} \mathrm{C}\), 1.5 bar. Assuming the compressor is well insulated, determine (a) the relative humidity at the exit. (b) the power input, in kW. (c) the rate of entropy production, in kW/K.

Moist air enters a control volume operating at steady state with a volumetric flow rate of \(3500 \mathrm{ft}^{3} / \mathrm{min}\). The moist air enters at \(120^{\circ} \mathrm{F}\), 1.2 atm, and 75% relative humidity. Heat transfer occurs through a surface maintained at \(50^{\circ} \mathrm{F}\). Saturated moist air and condensate exit the control volume, each at \(68^{\circ} \mathrm{F}\). Assuming \(\dot{W}_{\mathrm{cv}}=0\), and kinetic and potential energy effects are negligible, determine (a) the mass flow rate of condensate, in lb/min. (b) the rate of heat transfer, in Btu/min. (c) the rate of entropy production, in \(\mathrm{Btu} /{ }^{\circ} \mathrm{R} \cdot \min\). (d) the rate of exergy destruction, in Btu/min, for \(T_{0}=50^{\circ} \mathrm{F}\).

Moist air at \(15^{\circ} \mathrm{C}\), 1.3 atm, 63% relative humidity and a volumetric flow rate of \(770 \mathrm{m}^{3} / \mathrm{h}\) enters a control volume at steady state and flows along a surface maintained at \(187^{\circ} \mathrm{C}\), through which heat transfer occurs. Liquid water at \(15^{\circ} \mathrm{C}\) is injected at a rate of 7 kg/h and evaporates into the flowing stream. For the control volume, \(\dot{W}_{\mathrm{cv}}=0\), and kinetic and potential energy effects are negligible. If moist air exits at \(45^{\circ} \mathrm{C}\), 1.3 atm, determine (a) the rate of heat transfer, in kW. (b) the rate of entropy production, in kW/K.

Using Eq. 12.48, determine the humidity ratio and relative humidity for each case below. (a) The dry-bulb and wet-bulb temperatures in a conference room at 1 atm are 24 and \(16^{\circ} \mathrm{C}\), respectively. (b) The dry-bulb and wet-bulb temperatures in a factory space at 1 atm are 75 and \(60^{\circ} \mathrm{F}\), respectively. (c) Repeat parts (a) and (b) using the psychrometric chart. (d) Repeat parts (a) and (b) using Interactive Thermodynamics: IT.

Using the psychrometric chart, Fig. A-9, determine (a) the relative humidity, the humidity ratio, and the specific enthalpy of the mixture, in kJ per kg of dry air, corresponding to dry-bulb and wet-bulb temperatures of 30 and \(25^{\circ} \mathrm{C}\), respectively. (b) the humidity ratio, mixture specific enthalpy, and wetbulb temperature corresponding to a dry-bulb temperature of \(30^{\circ} \mathrm{C}\) and 60% relative humidity. (c) the dew point temperature corresponding to dry-bulb and wet-bulb temperatures of 30 and \(20^{\circ} \mathrm{C}\), respectively. (d) Repeat parts (a)–(c) using Interactive Thermodynamics: IT.

Using the psychrometric chart, Fig. A-9E, determine (a) the dew point temperature corresponding to dry-bulb and wet-bulb temperatures of 80 and \(70^{\circ} \mathrm{F}\), respectively. (b) the humidity ratio, the specific enthalpy of the mixture, in Btu per lb of dry air, and the wet-bulb temperature corresponding to a dry-bulb temperature of \(80^{\circ} \mathrm{F}\) and 70% relative humidity. (c) the relative humidity, humidity ratio, and mixture specific enthalpy corresponding to dry-bulb and wet-bulb temperatures of 80 and \(65^{\circ} \mathrm{F}\), respectively. (d) Repeat parts (a)–(c) using Interactive Thermodynamics: IT.

A fixed amount of air initially at \(52^{\circ} \mathrm{C}\), 1 atm, and 10% relative humidity is cooled at constant pressure to \(15^{\circ} \mathrm{C}\). Using the psychrometric chart, determine whether condensation occurs. If so, evaluate the amount of water condensed, in kg per kg of dry air. If there is no condensation, determine the relative humidity at the final state.

A fan within an insulated duct delivers moist air at the duct exit at \(35^{\circ} \mathrm{C}\), 50% relative humidity, and a volumetric flow rate of \(0.4 \mathrm{m}^{3} / \mathrm{s}\). At steady state, the power input to the fan is 1.7 kW. The pressure in the duct is nearly 1 atm throughout. Using the psychrometric chart, determine the temperature, in \({ }^{\circ} \mathrm{C}\), and relative humidity at the duct inlet.

The mixture enthalpy per unit mass of dry air, in kJ/kg(a), represented on Fig. A-9 can be approximated closely from the expression \(\frac{H}{m_{\mathrm{a}}}=1.005 T\left({ }^{\circ} \mathrm{C}\right)+\omega\left[2501.7+1.82 T\left({ }^{\circ} \mathrm{C}\right)\right]\) When using Fig. A-9E, the corresponding expression, in Btu/lb(a), is \(\frac{H}{m_{\mathrm{a}}}=0.24 T\left({ }^{\circ} \mathrm{F}\right)+\omega\left[1061+0.444 T\left({ }^{\circ} \mathrm{F}\right)\right]\) Noting all significant assumptions, develop the above expressions.

Each case listed gives the dry-bulb temperature and relative humidity of the moist air stream entering an airconditioning system: \(\begin{array}{l}\text{(a) } 40^{\circ} \mathrm{C}, 60 \%\\\text{(b) } 20^{\circ} \mathrm{C}, 65 \%\\\text{(c) } 32^{\circ} \mathrm{C}, 45 \%\\\text{(d) } 13^{\circ} \mathrm{C}, 30 \%\\\text{(e) } 30^{\circ} \mathrm{C}, 35 \%\end{array}\) The condition of the moist air stream exiting the system must satisfy these constraints: \(23 \leq T_{\mathrm{db}} \leq 28^{\circ} \mathrm{C}, 45 \leq \phi \leq 60 \%\). In each case, develop a schematic of equipment and process from Sec. 12.8 that would achieve the desired result. The processes might include combinations of cooling, dehumidification, heating, and humidification. Sketch the process on a psychrometic chart.

Moist air enters a device operating at steady state at 1 atm with a dry-bulb temperature of \(55^{\circ} \mathrm{C}\) and a wet-bulb temperature of \(25^{\circ} \mathrm{C}\). Liquid water at \(20^{\circ} \mathrm{C}\) is sprayed into the air stream, bringing it to 408C, 1 atm at the exit. Determine (a) the relative humidities at the inlet and exit. (b) the rate that liquid water is sprayed into the air stream, in kg per kg of dry air.

Air at 1 atm with dry-bulb and wet-bulb temperatures of 82 and \(68^{\circ} \mathrm{F}\), respectively, enters a duct with a mass flow rate of 10 lb/min and is cooled at essentially constant pressure to \(62^{\circ} \mathrm{F}\). For steady-state operation and negligible kinetic and potential energy effects, determine (a) the relative humidity at the duct inlet. (b) the rate of heat transfer, in Btu/min. (c) Check your answers using data from the psychrometric chart. (d) Check your answers using Interactive Thermodynamics: IT.

Air at \(35^{\circ} \mathrm{C}\), 1 atm, and 50% relative humidity enters a dehumidifier operating at steady state. Saturated moist air and condensate exit in separate streams, each at \(15^{\circ} \mathrm{C}\). Neglecting kinetic and potential energy effects, determine (a) the heat transfer from the moist air, in kJ per kg of dry air. (b) the amount of water condensed, in kg per kg of dry air. (c) Check your answers using data from the psychrometric chart. (d) Check your answers using Interactive Thermodynamics: IT.

Air at \(80^{\circ} \mathrm{F}\), 1 atm, and 70% relative humidity enters a dehumidifier operating at steady state with a mass flow rate of 1 lb/s. Saturated moist air and condensate exit in separate streams, each at \(50^{\circ} \mathrm{F}\). Neglecting kinetic and potential energy effects, determine (a) the rate of heat transfer from the moist air, in tons. (b) the rate water is condensed, in lb/s. (c) Check your answers using data from the psychrometric chart. (d) Check your answers using Interactive Thermodynamics: IT.

Moist air at \(28^{\circ} \mathrm{C}\), 1 bar, and 50% relative humidity flows through a duct operating at steady state. The air is cooled at essentially constant pressure and exits at \(20^{\circ} \mathrm{C}\). Determine the heat transfer rate, in kJ per kg of dry air flowing, and the relative humidity at the exit.

An air conditioner operating at steady state takes in moist air at \(28^{\circ} \mathrm{C}\), 1 bar, and 70% relative humidity. The moist air first passes over a cooling coil in the dehumidifier unit and some water vapor is condensed. The rate of heat transfer between the moist air and the cooling coil is 11 tons. Saturated moist air and condensate streams exit the dehumidifier unit at the same temperature. The moist air then passes through a heating unit, exiting at \(24^{\circ} \mathrm{C}\), 1 bar, and 40% relative humidity. Neglecting kinetic and potential energy effects, determine (a) the temperature of the moist air exiting the dehumidifier unit, in \({ }^{\circ} \mathrm{C}\). (b) the volumetric flow rate of the air entering the air conditioner, in \(\mathrm{m}^{3} / \mathrm{min}\). (c) the rate water is condensed, in kg/min. (d) the rate of heat transfer to the air passing through the heating unit, in kW.

Figure P12.82 shows a compressor followed by an aftercooler. Atmospheric air at \(14.7 \mathrm{lbf} / \mathrm{in}^{2}\), \(90^{\circ} \mathrm{F}\), and 75% relative humidity enters the compressor with a volumetric flow rate of \(100 \mathrm{ft}^{3} / \mathrm{min}\). The compressor power input is 15 hp. The moist air exiting the compressor at \(100 \mathrm{lbf} / \mathrm{in}^{2}\), \(400^{\circ} \mathrm{F}\) flows through the aftercooler, where it is cooled at constant pressure, exiting saturated at \(100^{\circ} \mathrm{F}\). Condensate also exits the aftercooler at \(100^{\circ} \mathrm{F}\). For steady-state operation and negligible kinetic and potential energy effects, determine (a) the rate of heat transfer from the compressor to its surroundings, in Btu/min. (b) the mass flow rate of the condensate, in lb/min. (c) the rate of heat transfer from the moist air to the refrigerant circulating in the cooling coil, in tons of refrigeration.

Outside air at \(50^{\circ} \mathrm{F}\), 1 atm, and 40% relative humidity enters an air-conditioning device operating at steady state. Liquid water is injected at 458F and a moist air stream exits with a volumetric flow rate of \(1000 \mathrm{ft}^{3} / \mathrm{min}\) at \(90^{\circ} \mathrm{F}\), 1 atm and a relative humidity of 40%. Neglecting kinetic and potential energy effects, determine (a) the rate water is injected, in lb/min. (b) the rate of heat transfer to the moist air, in Btu/h.

Figure P12.84 shows a steam-spray humidification device at steady state. Heat transfer between the device and its surroundings can be ignored, as can kinetic and potential energy effects. Determine the rate of exergy destruction, in Btu/min, for \(T_{0}=-95^{\circ} \mathrm{F}\).

Moist air at \(95^{\circ} \mathrm{F}\), 1 atm, and a relative humidity of 30% enters a steam-spray humidification device operating at steady state with a volumetric flow rate of \(5700 \mathrm{ft}^{3} / \mathrm{min}\). Saturated water vapor at \(230^{\circ} \mathrm{F}) is sprayed into the moist air, which then exits the device at a relative humidity of 50%. Heat transfer between the device and its surroundings can be ignored, as can kinetic and potential energy effects. Determine (a) the temperature of the exiting moist air stream, in \({ }^{\circ} \mathrm{F}\). (b) the rate at which steam is injected, in lb/min.

For the steam-spray humidifier in Problem 12.85, determine the exergy destruction rate, in Btu/min. Let \(T_{0}=-90^{\circ} \mathrm{F}\).

Atmospheric air having dry-bulb and wet-bulb temperatures of 33 and \(29^{\circ} \mathrm{C}\), respectively, enters a well-insulated chamber operating at steady state and mixes with air entering with dry-bulb and wet-bulb temperatures of 16 and \(12^{\circ} \mathrm{C}\), respectively. The volumetric flow rate of the lower temperature stream is twice that of the other stream. A single mixed stream exits. Determine for the exiting stream (a) the relative humidity. (b) the temperature, in \({ }^{\circ} \mathrm{C}\). Pressure is uniform throughout at 1 atm. Neglect kinetic and potential energy effects.

Moist air at \(27^{\circ} \mathrm{C}\), 1 atm, and 50% relative humidity enters an evaporative cooling unit operating at steady state consisting of a heating section followed by a soaked pad evaporative cooler operating adiabatically. The air passing through the heating section is heated to \(45^{\circ} \mathrm{C}\). Next, the air passes through a soaked pad exiting with 50% relative humidity. Using data from the psychrometric chart, determine (a) the humidity ratio of the entering moist air mixture, in kg(vapor) per kg(dry air). (b) the rate of heat transfer to the moist air passing through the heating section, in kJ per kg of mixture. (c) the humidity ratio and temperature, in \({ }^{\circ} \mathrm{C}\), at the exit of the evaporative cooling section.

At steady state, a stream consisting of \(650 \mathrm{ft}^{3} / \mathrm{min}\) of air at \(55^{\circ} \mathrm{F}\), 1 atm, 20% relative humidity is mixed adiabatically with a stream consisting of \(900 \mathrm{ft}^{3} / \mathrm{min}\) of air at \(75^{\circ} \mathrm{F}\), 1 atm, 80% relative humidity. A single mixed stream exits at 1 atm. Neglect kinetic and potential energy effects. Determine for the exiting stream (a) the relative humidity. (b) the temperature, in \({ }^{\circ} \mathrm{F}\).

At steady state, moist air is to be supplied to a classroom at a specified volumetric flow rate and temperature T. Air is removed from the classroom in a separate stream at a temperature of \(27^{\circ} \mathrm{C}\) and 50% relative humidity. Moisture is added to the air in the room from the occupants at a rate of 4.5 kg/h. The moisture can be regarded as saturated vapor at \(33^{\circ} \mathrm{C}\). Heat transfer into the occupied space from all sources is estimated to occur at a rate of 34,000 kJ/h. The pressure remains uniform at 1 atm. (a) For a supply air volumetric flow rate of \(40 \mathrm{m}^{3} / \mathrm{min}\), determine the supply air temperature T, in \({ }^{\circ} \mathrm{C}\), and the relative humidity. (b) Plot the supply air temperature, in \({ }^{\circ} \mathrm{C}\), and relative humidity, each versus the supply air volumetric flow rate ranging from 35 to \(90 \mathrm{m}^{3} / \mathrm{min}\).

At steady state, a device for heating and humidifying air has \(250 \mathrm{ft}^{3} / \mathrm{min}\) of air at \(40^{\circ} \mathrm{F}\), 1 atm, and 80% relative humidity entering at one location, \(1000 \mathrm{ft}^{3} / \mathrm{min}\) of air at \(60^{\circ} \mathrm{F}\), 1 atm, and 80% relative humidity entering at another location, and liquid water injected at \(55^{\circ} \mathrm{F}\). A single moist air stream exits at \(85^{\circ} \mathrm{F}\), 1 atm, and 35% relative humidity. Using data from the psychrometric chart, Fig. A-9E, determine (a) the rate of heat transfer to the device, in Btu/min. (b) the rate at which liquid water is injected, in lb/min. Neglect kinetic and potential energy effects.

Air at \(35^{\circ} \mathrm{C}\), 1 bar, and 10% relative humidity enters an evaporative cooler operating at steady state. The volumetric flow rate of the incoming air is \(50 \mathrm{m}^{3} / \mathrm{min}\). Liquid water at \(20^{\circ} \mathrm{C}\) enters the cooler and fully evaporates. Moist air exits the cooler at \(25^{\circ} \mathrm{C}\), 1 bar. If there is no significant heat transfer between the device and its surroundings, determine (a) the rate at which liquid enters, in kg/min. (b) the relative humidity at the exit. (c) the rate of exergy destruction, in kJ/min, for \(T_{0}=-20^{\circ} \mathrm{C}\). Neglect kinetic and potential energy effects.

Using Eqs. 12.56, show that \(\frac{\dot{m}_{\mathrm{a} 1}}{\dot{m}_{\mathrm{a} 2}}=\frac{\omega_{3}-\omega_{2}}{\omega_{1}-\omega_{3}}=\frac{\left(h_{\mathrm{a} 3}+\omega_{3} h_{\mathrm{g} 3}\right)-\left(h_{\mathrm{a} 2}+\omega_{2} h_{\mathrm{g} 2}\right)}{\left(h_{\mathrm{a} 1}+\omega_{1} h_{\mathrm{g} 1}\right)-\left(h_{\mathrm{a} 3}+\omega_{3} h_{\mathrm{g} 3}\right)}\) Employ this relation to demonstrate on a psychrometric chart that state 3 of the mixture lies on a straight line connecting the initial states of the two streams before mixing.

For the adiabatic mixing process in Example 12.14, plot the exit temperature, in \({ }^{\circ} \mathrm{C}\), versus the volumetric flow rate of stream 2 ranging from 0 to \(1400 \mathrm{m}^{3} / \mathrm{min}\). Discuss the plot as \((\mathrm{AV})_{2}\) goes to zero and as \((\mathrm{AV})_{2}\) becomes large.

A stream consisting of \(35 \mathrm{m}^{3} / \mathrm{min}\) of moist air at \(14^{\circ} \mathrm{C}\), 1 atm, 80% relative humidity mixes adiabatically with a stream consisting of \(80 \mathrm{m}^{3} / \mathrm{min}\) of moist air at \(40^{\circ} \mathrm{C}\), 1 atm, 40% relative humidity, giving a single mixed stream at 1 atm. Using the psychrometric chart together with the procedure of Problem 12.93, determine the relative humidity and temperature, in \({ }^{\circ} \mathrm{C}\), of the exiting stream.

At steady state, a stream of air at \(56^{\circ} \mathrm{F}\), 1 atm, 50% relative humidity is mixed adiabatically with a stream of air at \(100^{\circ} \mathrm{F}\), 1 atm, 80% relative humidity. The mass flow rate of the higher-temperature stream is twice that of the other stream. A single mixed stream exits at 1 atm. Using the result of Problem 12.74, determine for the exiting stream (a) the temperature, in \({ }^{\circ} \mathrm{F}). (b) the relative humidity. Neglect kinetic and potential energy effects.

At steady state, moist air at \(42^{\circ} \mathrm{C}\), 1 atm, 30% relative humidity is mixed adiabatically with a second moist air stream entering at 1 atm. The mass flow rates of the two streams are the same. A single mixed stream exits at \(29^{\circ} \mathrm{C}\), 1 atm, 40% relative humidity with a mass flow rate of 2 kg/s. Kinetic and potential energy effects are negligible. For the second entering moist air stream, determine, using data from the psychrometric chart, (a) the relative humidity. (b) the temperature, in \({ }^{\circ} \mathrm{C}\).

Figure P12.98 shows two options for conditioning atmospheric air at steady state. In each case, air enters at \(15^{\circ} \mathrm{C}\), 1 atm, and 20% relative humidity with a volumetric flow rate of \(150 \mathrm{m}^{3} / \mathrm{min}\) and exits at \(30^{\circ} \mathrm{C}\), 1 atm, and 40% relative humidity. One method conditions the air by injecting saturated water vapor at 1 atm. The other method allows the entering air to pass through a soaked pad replenished by liquid water entering at \(20^{\circ} \mathrm{C}\). The moist air stream is then heated by an electric resistor. For \(T_{0}=-288 \mathrm{K}\), which of the two options is preferable from the standpoint of having less exergy destruction? Discuss.

Air at \(30^{\circ} \mathrm{C}\), 1 bar, 50% relative humidity enters an insulated chamber operating at steady state with a mass flow rate of 3 kg/min and mixes with a saturated moist air stream entering at \(5^{\circ} \mathrm{C}\), 1 bar with a mass flow rate of 5 kg/min. A single mixed stream exits at 1 bar. Determine (a) the relative humidity and temperature, in \({ }^{\circ} \mathrm{C}\), of the exiting stream. (b) the rate of exergy destruction, in kW, for \(T_{0}=-20^{\circ} \mathrm{C}\). Neglect kinetic and potential energy effects.

Figure P12.100 shows a device for conditioning moist air entering at \(5^{\circ} \mathrm{C}\), 1 atm, 90% relative humidity, and a volumetric flow rate of \(60 \mathrm{m}^{3} / \mathrm{min}\). The incoming air is first heated at essentially constant pressure to \(24^{\circ} \mathrm{C}\). Superheated steam at 1 atm is then injected, bringing the moist air stream to \(25^{\circ} \mathrm{C}\), 1 atm, and 45% relative humidity. Determine for steady-state operation (a) the rate of heat transfer to the air passing through the heating section, in kJ/min. (b) the mass flow rate of the injected steam, in kg/min. (c) If the injected steam expands through a valve from a saturated vapor condition at the valve inlet, determine the inlet pressure, in bar. Neglect kinetic and potential energy effects.

A stream of air (stream 1) at \(60^{\circ} \mathrm{F}\), 1 atm, 30% relative humidity is mixed adiabatically with a stream of air (stream 2) at \(90^{\circ} \mathrm{F}\), 1 atm, 80% relative humidity. A single stream (stream 3) exits the mixing chamber at temperature \(T_{3}\) and 1 atm. Assume steady state and ignore kinetic and potential energy effects. Letting r denote the ratio of dry air mass flow rates \(\dot{m}_{\mathrm{a} 1} / \dot{m}_{\mathrm{a} 2}\) (a) determine \(T_{3} \text {, in }{ }^{\circ} \mathrm{F}\), for r = 2. (b) plot \(T_{3} \text {, in }{ }^{\circ} \mathrm{F}\), versus r ranging from 0 to 10.

Figure P12.102 shows the adiabatic mixing of two moist-air streams at steady state. Kinetic and potential energy effects are negligible. Determine the rate of exergy destruction, in Btu/min, for \(T_{0}=-95^{\circ} \mathrm{F}\).

In the condenser of a power plant, energy is discharged by heat transfer at a rate of 836 MW to cooling water that exits the condenser at \(40^{\circ} \mathrm{C}\) into a cooling tower. Cooled water at \(20^{\circ} \mathrm{C}\) is returned to the condenser. Atmospheric air enters the tower at \(25^{\circ} \mathrm{C}\), 1 atm, 35% relative humidity. Moist air exits at \(35^{\circ} \mathrm{C}\), 1 atm, 90% relative humidity. Makeup water is supplied at \(20^{\circ} \mathrm{C}\). For operation at steady state, determine the mass flow rate, in kg/s, of (a) the entering atmospheric air. (b) the makeup water. Ignore kinetic and potential energy effects.

Liquid water at \(100^{\circ} \mathrm{F}\) enters a cooling tower operating at steady state, and cooled water exits the tower at \(80^{\circ} \mathrm{F}\). Data for the various streams entering and exiting the tower are shown in Fig. P12.104. No makeup water is provided. Determine (a) the mass flow rate of the entering atmospheric air, in lb/h. (b) the rate at which water evaporates, in lb/h. (c) the mass flow rate of the exiting liquid stream, in lb/h.

Liquid water at \(150^{\circ} \mathrm{F}\) enters a cooling tower operating at steady state with a mass flow rate of 140 lb/s. Atmospheric air enters at \(80^{\circ} \mathrm{F}\), 1 atm, 30% relative humidity. Saturated air exits at \(100^{\circ} \mathrm{F}\), 1 atm. Makeup water is not provided. Determine the mass flow rate of dry air required, in lb/h, if cooled water exits the tower at (a) \(80^{\circ} \mathrm{F}\) and (b) \(60^{\circ} \mathrm{F}\). Ignore kinetic and potential energy effects.

Liquid water at \(100^{\circ} \mathrm{F}\) and a volumetric flow rate of 200 gal/min enters a cooling tower operating at steady state. Atmospheric air enters at 1 atm with a dry-bulb temperature of \(80^{\circ} \mathrm{F}\) and a wet-bulb temperature of \(60^{\circ} \mathrm{F}\). Moist air exits the cooling tower at \(90^{\circ} \mathrm{F}\) and 90% relative humidity. Makeup water is provided at \(80^{\circ} \mathrm{F}\). Plot the mass flow rates of the dry air and makeup water, each in lb/min, versus return water temperature ranging from 80 to \(100^{\circ} \mathrm{F}\). Ignore kinetic and potential energy effects.

Liquid water enters a cooling tower operating at steady state at \(40^{\circ} \mathrm{C}\) with a mass flow rate of 105 kg/h. Cooled water at \(25^{\circ} \mathrm{C}\) exits the cooling tower at the same mass flow rate. Makeup water is supplied at \(23^{\circ} \mathrm{C}\). Atmospheric air enters the tower at \(30^{\circ} \mathrm{C}\), 1 bar, 35% relative humidity. A saturated moist air stream exits at \(34^{\circ} \mathrm{C}\), 1 bar. Determine (a) the mass flow rates of the dry air and makeup water, each in kg/h. (b) the rate of exergy destruction within the cooling tower, in kW, for \(T_{0}=-23^{\circ} \mathrm{C}\). Ignore kinetic and potential energy effects.

Liquid water at \(120^{\circ} \mathrm{F}\) and a volumetric flow rate of \(275 \mathrm{ft}^{3} / \mathrm{min}\) enters a cooling tower operating at steady state. Cooled water exits the cooling tower at \(90^{\circ} \mathrm{F}\). Atmospheric air enters the tower at \(86^{\circ} \mathrm{F}\), 1 atm, 35% relative humidity, and saturated moist air at \(100^{\circ} \mathrm{F}\), 1 atm exits the cooling tower. Determine (a) the mass flow rates of the dry air and the cooled water, each in lb/min. (b) the rate of exergy destruction within the cooling tower, in Btu/s, for \(T_{0}=-77^{\circ} \mathrm{F}\). Ignore kinetic and potential energy effects.

About half the air we breathe on some airplanes is fresh air, and the rest is recirculated. Investigate typical equipment schematics for providing a blend of fresh and recirculated filtered air to the passenger cabins of commercial airplanes. What types of filters are used and how do they work? Write a report including at least three references.

Identify a campus, commercial, or other building in your locale with an air-conditioning system installed 20 or more years ago. Critically evaluate the efficacy of the system in terms of comfort level provided, operating costs, maintenance costs, global warming potential of the refrigerant used, and other pertinent issues. On this basis, recommend specific system upgrades or a full system replacement, as warranted. Present your findings in a PowerPoint presentation.

Study the air-conditioning system for one of the classrooms you frequent where occupant comfort is unsatisfactory and describe the system in detail, including the control strategy used. Propose modifications aimed at improving occupant satisfaction, including a new heating, ventilation, and air conditioning (HVAC) system for the room, if warranted. Compare the proposed and existing systems in terms of occupant comfort, potential impact on productivity, and energy requirements. Detail your findings in an executive summary and PowerPoint presentation.

Critically evaluate a cooling tower on your campus, or nearby, in terms of effectiveness in providing the required range of cooled water, operating costs, maintenance costs, and other relevant issues. If warranted, recommend cost-effective upgrades of the existing cooling tower or alternative cooling technologies to achieve the desired level of performance, including options for minimizing water loss. Present your findings in a report including at least three references.

Supermarkets in the United States use air-conditioning systems that are usually designed primarily to control temperature, and these typically produce a relative humidity of about 55%. At this relative humidity, excessive frost and condensation can form inside refrigerated display cases, and a substantial amount of energy must be expended to avoid these problems. Investigate technologies available for reducing overall store humidity levels within supermarkets to 40–45%, thereby reducing problems associated with frost and condensation. Estimate the potential operating cost saving associated with such a strategy for a supermarket within your locale. Refrigerated display cases with glass-door fronts can significantly reduce the refrigeration load. What are the associated impacts on the overall store humidity level and the occurrence of frost and condensation forming within the closed cases? Write a report including sample calculations and at least three references.

The human body regulates its temperature under various relative humidity, pressure, and temperature conditions using thermoregulation mechanisms. Explore the designs of space suits that are worn inside a spacecraft and those worn outside a spacecraft. How are such clothing systems designed to provide protection against the harsh environment of outer space while maintaining sufficient thermal comfort to allow for strenuous physical activity? Include in your report at least three references.

Phosphorous compounds and zinc are used as additives in larger cooling tower systems to control corrosion and deposition of solids. Regulations are emerging that will limit the use of phosphorous compounds in these systems, especially those discharging process water directly to public waterways. Write a report explaining how cooling towers are maintained. Include relevant chemistry and explore how corrosion and deposition are currently controlled. Examine emerging regulations and describe ways by which new and existing designs will need to be modified to comply with new regulations. Include in your report at least three references.

Nearly 20 years ago, eight scientists entered Biosphere 2, located in Oracle, Arizona, for a planned two-year period of isolation. The three-acre biosphere had several ecosystems, including a desert, tropical rain forest, grassland, and saltwater wetlands. It also included species of plants and microorganisms intended to sustain the ecosystems. According to plan, the scientists would produce their own food using intensive organic farming, fish farmed in ponds, and a few barnyard animals. Occupants also would breathe oxygen produced by the plants and drink water cleansed by natural processes. Sunlight and a natural gas–fueled generator were to meet all energy needs. Numerous difficulties were encountered with the ecosystems and by the scientists, including insufficient oxygen, hunger and loss of body weight, and animosities among individuals. Study the record of Biosphere 2 for lessons that would substantially assist in designing a self-sustaining enclosed biosphere for human habitation on Mars. Present your results in a report including at least three references.

In a 2007 study using influenza-infected guinea pigs in climate-controlled habitats, researchers investigated the aerosol transmission of influenza virus while varying the temperature and humidity within the habitats. The research showed there were more infections when it was colder and drier, and based on this work a significant correlation was found between humidity ratio and influenza. (See BIOCONNECTIONS on p. 756) For the aerosol transmission experiments, guinea pigs were housed within cabinets like the one shown in Fig. P12.9D. Each cabinet is fitted with a dedicated compressed-air line and an associated compressed-air dryer that provides precise and rapid control for the cabinet’s humidity injection and dehumidification systems. A condensate recirculator collects and recycles the condensate that forms in the base of the chamber and provides continuous, clean, filtered water to the cabinet’s humidity injection system. The cabinets were placed within an isolated room with an ambient temperature of approximately \(20^{\circ} \mathrm{C}\). Experimenters say ambient temperatures in excess of \(25^{\circ} \mathrm{C}\) can result in chamber failure. The objective of this project is to specify the heating, ventilation, and air conditioning (HVAC) system for the room housing the cabinets, assuming the room encompasses \(500 \mathrm{ft} / \mathrm{s}^{2}\) and houses five environmental cabinets with up to eight guinea pigs per cabinet. Each cabinet delivers a maximum heat transfer rate of 4000 Btu/h to the room. Document your design in a report including a minimum of three references that substantiate assumptions made during the design process.

Building energy use is significant in the United States, consuming about 70% of all electricity generated. An increase in electricity use of about 50% is expected by the end of the current decade. In response to the adverse impact that buildings have on energy use and the environment, in 1998 the U.S. Green Building Council developed LEED® (Leadership in Energy and Environmental Design), a certification system aimed at improving the performance of buildings across several measures, including energy and water use, greenhouse gas emission, and indoor environmental quality. Thousands of buildings throughout the world have now gained LEED® certification. Identify a newly constructed LEED®-certified building on your campus or in a nearby locale. Determine the level of LEED® certification the building achieves: certified, silver, gold, or platinum. Prepare a summary of the building’s design, focusing on elements incorporated to improve building energy and environmental performance and associated costs. Present your findings in a written report including at least three references.

In 2010, the U.S. Department of Energy focused its research agenda on innovative technologies to provide energy-efficient cooling for buildings and reduce greenhouse gas emissions. Key agenda items include developing the following: 1. Cooling systems using refrigerants with global warming potential less than or equal to 1 2. Air-conditioning systems for warm and humid climates that increase the coefficient of performance of ventilation air cooling by 50% or more, based on current technology 3. Hot-climate vapor-compression air-conditioning systems that condition recirculated air while increasing the coefficient of performance by 50% or more, based on current technology For one such project supported by the Department of Energy, prepare a report that summarizes the project goals and objectives, research plan, and expected outcomes. Also critically evaluate the feasibility of incorporating the resulting technology into existing cooling systems.

An air-handling system is being designed for a 40 ft X 40 ft X 8 ft biological research facility that houses 3000 laboratory mice. The indoor conditions must be maintained at \(75^{\circ} \mathrm{F}\), 60% relative humidity when the outdoor air conditions are \(90^{\circ} \mathrm{F}\), 70% relative humidity. Develop a preliminary design of an air-conditioning and distribution system that satisfies National Institutes of Health (NIH) standards for animal facilities. Assume a biological safety level of one (BSL-1), and that two-thirds of the floor space is devoted to animal care. Since an interruption in ventilation or air conditioning could place the laboratory animals under stress and compromise the research under way in the facility, account for redundancy in your design.

Adequate levels of ventilation reduce the likelihood of sick building syndrome. (See BIOCONNECTIONS on p. 753.) The outdoor air used for ventilation must be conditioned, and this requires energy. Consider the airhandling system for the commercial building illustrated in Fig. P12.13D, consisting of ducting, two dampers labeled A and B, a vapor-compression dehumidifier, and a heater. The system supplies \(25 \mathrm{m}^{3} / \mathrm{s}\) of conditioned air at \(20^{\circ} \mathrm{C}\) and a relative humidity of 55% to maintain the interior space at \(25^{\circ} \mathrm{C}\) and a relative humidity of 50%. The recirculated air has the same conditions as the air in the interior space. A minimum of \(5 \mathrm{m}^{3} / \mathrm{s}\) of outdoor air is required to provide adequate ventilation. Dampers A and B can be set to provide alternative operating modes to maintain required ventilation rates. On a given summer day when the outside air dry-bulb temperature and relative humidity are \(25^{\circ} \mathrm{C}\) and 60%, respectively, which of the following three operating modes is best from the standpoint of minimizing the total heat transfer of energy from the conditioned air to the cooling coil and to the conditioned air from the heating coil? 1. Dampers A and B closed. 2. Damper A open and damper B closed with outside air contributing one-quarter of the total supply air. 3. Dampers A and B open. One-quarter of the conditioned air comes from outside air and one-third of the recirculated air bypasses the dehumidifier via open damper B; the rest flows through damper A. Present your recommendation together with your reasoning in a PowerPoint presentation suitable for your class. Additionally, in an accompanying memorandum, provide well-documented sample calculations in support of your recommendation.