Solution Found!
Energy Analysis of Control Volumes at Steady
Chapter 4, Problem 58P(choose chapter or problem)
Air enters a compressor operating at steady state with a pressure of \(14.7 \mathrm{lbf} / \mathrm{in}^2\), a temperature of \(80^{\circ} \mathrm{F}\), and a volumetric flow rate of \(18 \mathrm{ft}^3 / \mathrm{s}\). The air exits the compressor at a pressure of \(90 \mathrm{lbf} / \mathrm{in} .{ }^2\) Heat transfer from the compressor to its surroundings occurs at a rate of \(9.7 \mathrm{Btu}\) per lb of air flowing. The compressor power input is \(90 \mathrm{hp}\). Neglecting kinetic and potential energy effects and modeling air as an ideal gas, determine the exit temperature, in \({ }^{\circ} \mathrm{F}\).
Questions & Answers
QUESTION:
Air enters a compressor operating at steady state with a pressure of \(14.7 \mathrm{lbf} / \mathrm{in}^2\), a temperature of \(80^{\circ} \mathrm{F}\), and a volumetric flow rate of \(18 \mathrm{ft}^3 / \mathrm{s}\). The air exits the compressor at a pressure of \(90 \mathrm{lbf} / \mathrm{in} .{ }^2\) Heat transfer from the compressor to its surroundings occurs at a rate of \(9.7 \mathrm{Btu}\) per lb of air flowing. The compressor power input is \(90 \mathrm{hp}\). Neglecting kinetic and potential energy effects and modeling air as an ideal gas, determine the exit temperature, in \({ }^{\circ} \mathrm{F}\).
ANSWER:Step 1 of 2
We have to determine the exit temperature of air from a compressor.
The exit temperature can be determined by finding the enthalpy of the air as it exits the compressor using the steady state energy rate balance equation.
The kinetic and potential energy effects can be neglected,so the last two terms are equal to zero.
Hence,
where,
and
are the enthalpy of the air at inlet
and exit of the compressor in Btu/lb
Heat transfer rate = 9.7 Btu/min
compressor power input = -90 hp
mass flow rate in lb/s
The mass flow rate can be found using the expression,
From ideal gas equation of state
Thus,
Here,
Hence,
