Solved: A nuclear power plant has an electrical power

An ideal gas is maintained at a constant pressure of 70.0 kPa during an isobaric process while its volume decreases by 0.20 m3. What is the work done by the system on its environment? (a) 14 kJ (b) 35 kJ (c) _14 kJ (d) _35 kJ (e) _72 kJ

A 2.0-mole ideal gas system is maintained at a constant volume of 4.0 liters. If 100 J of thermal energy is transferred to the system, what is the change in the internal energy of the system? (a) 0 (b) 400 J (c) 70 J (d) 100 J (e) _0.100 J

A monatomic ideal gas expands from 1.00 m3 to 2.50 m3 at a constant pressure of 2.00 _ 105 Pa. Find the change in the internal energy of the gas. (a) 7.50 _ 105 J (b) 1.05 _ 106 J (c) 4.50 _ 105 J (d) 3.00 _ 105 J (e) _4.50 _ 105 J

An ideal gas drives a piston as it expands from 1.00 m3 to 2.00 m3 at a constant temperature of 850 K. If there are 390 moles of gas in the piston, how much work does the gas do in displacing the piston? (a) 1.9 _ 106 J (b) 2.5 _ 106 J (c) 4.7 _ 106 J (d) 2.1 _ 105 J (e) 3.5 _ 106 J

A diatomic ideal gas expands adiabatically from a volume of 1.00 m3 to a fi nal volume of 3.50 m3. If the initial pressure is 1.00 _ 105 Pa, what is the fi nal pressure? (a) 6.62 _ 104 Pa (b) 1.24 _ 105 Pa (c) 3.54 _ 104 Pa (d) 2.33 _ 104 Pa (e) 1.73 _ 104 Pa

How much net work is done by the gas undergoing the cyclic process illustrated in Figure MCQ12.6? Choose the best estimate. (a) 1 _ 105 J (b) 2 _ 105 J (c) 3 _ 105 J (d) 4 _ 105 J (e) 5 _ 105 Pa

An engine does 15 kJ of work while rejecting 37 kJ to the cold reservoir. What is the effi ciency of the engine? (a) 0.15 (b) 0.29 (c) 0.33 (d) 0.45 (e) 1.2

A refrigerator does 18 kJ of work while moving 115 kJ of thermal energy from inside the refrigerator. What is its coeffi cient of performance? (a) 3.4 (b) 2.8 (c) 8.9 (d) 6.4 (e) 5.2

A steam turbine operates at a boiler temperature of 450 K and an exhaust temperature of 3.0 _ 102 K. What is the maximum theoretical effi ciency of this system? (a) 0.24 (b) 0.50 (c) 0.33 (d) 0.67 (e) 0.15

A 1.00-kg block of ice at 0 C and 1.0 atm melts completely to water at 0C. Calculate the change of the entropy of the ice during the melting process. (For ice, Lf _ 3.33 _ 105 J/kg.) (a) 3 340 J/K (b) 2 170 J/K (c) _3 340 J/K (d) 1 220 J/K (e) _1 220 J/K

If an ideal gas is compressed isothermally, which of the following statements is true? (a) Energy is transferred to the gas by heat. (b) No work is done on the gas. (c) The temperature of the gas increases. (d) The internal energy of the gas remains constant. (e) The pressure remains constant.

When an ideal gas undergoes an adiabatic expansion, which of the following statements is true? (a) The temperature of the gas doesnt change. (b) No work is done by the gas. (c) No energy is delivered to the gas by heat. (d) The internal energy of the gas doesnt change. (e) The pressure increases.

If an ideal gas undergoes an isobaric process, which of the following statements is true? (a) The temperature of the gas doesnt change. (b) Work is done on or by the gas. (c) No energy is transferred by heat to or from the gas. (d) The volume of the gas remains the same. (e) The pressure of the gas decreases uniformly.

Of the following, which is not a statement of the second law of thermodynamics? (a) No heat engine operating in a cycle can absorb energy from a reservoir and use it entirely to do work. (b) No real engine operating between two energy reservoirs can be more effi cient than a Carnot engine operating between the same two reservoirs. (c) When a system undergoes a change in state, the change in the internal energy of the system is the sum of the energy transferred to the system by heat and the work done on the system. (d) The entropy of the Universe increases in all natural processes. (e) In all real processes, the resulting energy available for doing work decreases.

If an ideal gas is compressed to half its initial volume, which of the following statements is true regarding the work done on the gas? (a) The isothermal process involves the most work. (b) The adiabatic process involves the most work. (c) The isobaric process involves the most work. (d) The isovolumetric process involves the most work. (e) The work done is independent of the process.

A window air conditioner is placed on a table inside a well-insulated apartment, plugged in and turned on. What happens to the average temperature of the apartment? (a) It increases. (b) It decreases. (c) It remains constant. (d) It increases until the unit warms up and then decreases. (e) The answer depends on the initial temperature of the apartment.

The second law of thermodynamics implies that the coeffi cient of performance of a refrigerator must be what? (a) less than 1 (b) less than or equal to 1 (c) greater than or equal to 1 (d) fi nite (e) greater than 0

A thermodynamic process occurs in which the entropy of a system changes by -6 J/K. According to the second law of thermodynamics, what can you conclude about the entropy change of the environment? (a) It must be _6 J/K or less. (b) It must be equal to 6 J/K. (c) It must be between 6 J/K and 0. (d) It must be 0. (e) It must be _6 J/K or more.

What are some factors that affect the effi ciency of automobile engines?

If you shake a jar full of jelly beans of different sizes, the larger beans tend to appear near the top and the smaller ones tend to fall to the bottom. Why does that occur? Does this process violate the second law of thermodynamics?

For an ideal gas in an isothermal process, there is no change in internal energy. Suppose the gas does work W during such a process. How much energy was transferred by heat?

Clearly distinguish among temperature, heat, and internal energy.

Consider the human body performing a strenuous exercise, such as lifting weights or riding a bicycle. Work is being done by the body, and energy is leaving by conduction from the skin into the surrounding air. According to the fi rst law of thermodynamics, the temperature of the body should be steadily decreasing during the exercise. That isnt what happens, however. Is the fi rst law invalid for this situation? Explain.

A steam-driven turbine is one major component of an electric power plant. Why is it advantageous to increase the temperature of the steam as much as possible?

When a sealed Thermos bottle full of hot coffee is shaken, what changes, if any, take place in (a) the temperature of the coffee and (b) its internal energy?

In solar ponds constructed in Israel, the Suns energy is concentrated near the bottom of a salty pond. With the proper layering of salt in the water, convection is prevented and temperatures of 100 C may be reached. Can you guess the maximum effi ciency with which useful mechanical work can be extracted from the pond?

Is it possible to construct a heat engine that creates no thermal pollution?

If a supersaturated sugar solution is allowed to evaporate slowly, sugar crystals form in the container. Hence, sugar molecules go from a disordered form (in solution) to a highly ordered, crystalline form. Does this process violate the second law of thermodynamics? Explain.

The fi rst law of thermodynamics says we cant get more out of a process than we put in, but the second law says that we cant break even. Explain this statement.

Give some examples of irreversible processes that occur in nature. Give an example of a process in nature that is nearly reversible.

A gas changes in volume from 0.750 m3 to 0.250 m3 at a constant pressure of 1.50 _ 105 Pa. (a) How much work is done on the gas? (b) How much work is done by the gas on its environment? (c) Which of Newtons laws best explains why the work done on the gas is the negative of the work done on the environment?

Sketch a PV diagram and fi nd the work done by the gas during the following stages. (a) A gas is expanded from a volume of 1.0 L to 3.0 L at a constant pressure of 3.0 atm. (b) The gas is then cooled at constant volume until the pressure falls to 2.0 atm. (c) The gas is then compressed at a constant pressure of 2.0 atm from a volume of 3.0 L to 1.0 L. (Note: Be careful of signs.) (d) The gas is heated until its pressure increases from 2.0 atm to 3.0 atm at a constant volume. (e) Find the net work done during the complete cycle.

Gas in a container is at a pressure of 1.5 atm and a volume of 4.0 m3. What is the work done on the gas (a) if it expands at constant pressure to twice its initial volume, and (b) if it is compressed at constant pressure to onequarter its initial volume?

A 40.0-g projectile is launched by the expansion of hot gas in an arrangement shown in Figure P12.4a. The cross-sectional area of the launch tube is 1.0 cm2, and the length that the projectile travels down the tube after starting from rest is 32 cm. As the gas expands, the pressure varies as shown in Figure P12.4b. The values for the initial pressure and volume are Pi _ 11 _ 105 Pa and Vi _ 8.0 cm3 while the fi nal values are Pf _ 1.0 _ 105 Pa and Vf _ 40.0 cm3. Friction between the projectile and the launch tube is negligible. (a) If the projectile is launched into a vacuum, what is the speed of the projectile as it leaves the launch tube? (b) If instead the projectile is launched into air at a pressure of 1.0 _ 105 Pa, what fraction of the work done by the expanding gas in the tube is spent by the projectile pushing air out of the way as it proceeds down the tube?

A gas expands from I to F along the three paths indicated in Figure P12.5. Calculate the work done on the gas along paths (a) IAF, (b) IF, and (c) IBF.

Sketch a PV diagram of the following processes: (a) A gas expands at constant pressure P1 from volume V1 to volume V2. It is then kept at constant volume while the pressure is reduced to P2. (b) A gas is reduced in pressure from P1 to P2 while its volume is held constant at V1. It is then expanded at constant pressure P2 to a fi nal volume V2. (c) In which of the processes is more work done by the gas? Why?

A sample of helium behaves as an ideal gas as it is heated at constant pressure from 273 K to 373 K. If 20.0 J of work is done by the gas during this process, what is the mass of helium present?

One mole of an ideal gas initially at a temperature of 1.50 _ 102 C is compressed at a constant pressure of 2.00 atm to two-thirds its initial volume. (a) What is the fi nal temperature of the gas? (b) Calculate the work done on the gas during the compression.

One mole of an ideal gas initially at a temperature of Ti _ 0 C undergoes an expansion at a constant pressure of 1.00 atm to four times its original volume. (a) Calculate the new temperature Tf of the gas. (b) Calculate the work done on the gas during the expansion.

(a) Determine the work done on a fl uid that expands from i to f as indicated in Figure P12.10. (b) How much work is done on the fl uid if it is compressed from f to i along the same path?

The only form of energy possessed by molecules of a monatomic ideal gas is translational kinetic energy. Using the results from the discussion of kinetic theory in Section 10.5, show that the internal energy of a monatomic ideal gas at pressure P and occupying volume V may be written as U 5 32 PV .

A cylinder of volume 0.300 m3 contains 10.0 mol of neon gas at 20.0 C. Assume neon behaves as an ideal gas. (a) What is the pressure of the gas? (b) Find the internal energy of the gas. (c) Suppose the gas expands at constant pressure to a volume of 1.000 m3. How much work is done on the gas? (d) What is the temperature of the gas at the new volume? (e) Find the internal energy of the gas when its volume is 1.000 m3. (f) Compute the change in the internal energy during the expansion. (g) Compute _U _ W. (h) Must thermal energy be transferred to the gas during the constant pressure expansion or be taken away? (i) Compute Q, the thermal energy transfer. ( j) What symbolic relationship between Q, _U, and W is suggested by the values obtained?

A gas expands from I to F in Figure P12.5. The energy added to the gas by heat is 418 J when the gas goes from I to F along the diagonal path. (a) What is the change in internal energy of the gas? (b) How much energy must be added to the gas by heat for the indirect path IAF to give the same change in internal energy?

A thermodynamic system undergoes a process in which its internal energy decreases by 500 J. If at the same time 220 J of work is done on the system, fi nd the energy transferred to or from it by heat.

A gas is compressed at a constant pressure of 0.800 atm from 9.00 L to 2.00 L. In the process, 400 J of energy leaves the gas by heat. (a) What is the work done on the gas? (b) What is the change in its internal energy?

A quantity of a monatomic ideal gas undergoes a process in which both its pressure and volume are doubled as shown in Figure P12.16. What is the energy absorbed by heat into the gas during this process? (Hint: See Problem 11.)

A gas is enclosed in a container fi tted with a piston of cross-sectional area 0.150 m2. The pressure of the gas is maintained at 6 000 Pa as the piston moves inward 20.0 cm. (a) Calculate the work done by the gas. (b) If the internal energy of the gas decreases by 8.00 J, fi nd the amount of heat removed from the system by heat during the compression.

A monatomic ideal gas undergoes the thermodynamic process shown in the PV diagram of Figure P12.18. Determine whether each of the values _U, Q, and W for the gas is positive, negative, or zero. (Hint: See Problem 11.)

An ideal gas in a cylinder is compressed very slowly to one-third its original volume while its temperature is held constant. The work required to accomplish this task is 75 J. (a) What is the change in the internal energy of the gas? (b) How much energy is transferred to the gas by heat in this process?

An ideal gas in a cylinder is compressed adiabatically to one-half its original volume. The work required to compress the gas is 125 J. (a) How much energy is transferred into or out of the gas by heat in this process? (b) What is the change in the internal energy of the gas?

An ideal monatomic gas expands isothermally from 0.500 m3 to 1.25 m3 at a constant temperature of 675 K. If the initial pressure is 1.00 _ 105 Pa, fi nd (a) the work done on the gas, (b) the thermal energy transfer Q, and (c) the change in the internal energy.

An ideal gas expands at constant pressure. (a) Show that P _V _ nR _T. (b) If the gas is monatomic, start from the defi nition of internal energy and show that DU 5 32 Wenv, where Wenv is the work done by the gas on its environment. (c) For the same monatomic ideal gas, show with the fi rst law that Q 5 52 Wenv. (d) Is it possible for an ideal gas to expand at constant pressure while exhausting thermal energy? Explain.

One gram of water changes to ice at a constant pressure of 1.00 atm and a constant temperature of 0 C. In the process, the volume changes from 1.00 cm3 to 1.09 cm3. (a) Find the work done on the water and (b) the change in the internal energy of the water.

Consider the cyclic process described by Figure P12.24. If Q is negative for the process BC and _U is negative for the process CA, determine the signs of Q, W, and _U associated with each process. process shown in the PV diagram of Figure P12.18. Determine whether each of the values _U, Q, and W for the gas is positive, negative, or zero. (Hint: See Problem 11.)

A 5.0-kg block of aluminum is heated from 20 C to 90 C at atmospheric pressure. Find (a) the work done by the aluminum, (b) the amount of energy transferred to it by heat, and (c) the increase in its internal energy.

One mole of gas initially at a pressure of 2.00 atm and a volume of 0.300 L has an internal energy equal to 91.0 J. In its fi nal state, the gas is at a pressure of 1.50 atm and a volume of 0.800 L, and its internal energy equals 180 J. For the paths IAF, IBF, and IF in Figure P12.26, calculate (a) the work done on the gas and (b) the net energy transferred to the gas by heat in the process.

Consider the Universe to be an adiabatic expansion of atomic hydrogen gas. (a) Use the ideal gas law and Equation 12.8a to show that TV __1 _ C, where C is a constant. (b) The current Universe extends at least 15 billion light-years in all directions (1.4 _ 1026 m), and the current temperature of the Universe is 2.7 K. Estimate the temperature of the Universe when its was the size of a nutshell, with a radius of 2 cm. (For this calculation, assume the Universe is spherical.)

Suppose the Universe is considered to be an ideal gas of hydrogen atoms expanding adiabatically. (a) If the density of the gas in the Universe is one hydrogen atom per cubic meter, calculate the number of moles per unit volume (n/V). (b) Calculate the pressure of the Universe, taking the temperature of the Universe as 2.7 K. (c) If the current radius of the Universe is 15 billion light-years (1.4 _ 1026 m), fi nd the pressure of the Universe when it was the size of a nutshell, with radius 2.0 _ 10_2 m. Be careful: Calculator overfl ow can occur.

A gas increases in pressure from 2.00 atm to 6.00 atm at a constant volume of 1.00 m3 and then expands at constant pressure to a volume of 3.00 m3 before returning to its initial state as shown in Figure P12.29. How much work is done in one cycle?

An ideal gas expands at a constant pressure of 6.00 _ 105 Pa from a volume of 1.00 m3 to a volume of 4.00 m3 and then is compressed to one-third that pressure and a volume of 2.50 m3 as shown in Figure P12.30 before returning to its initial state. How much work is done in taking a gas through one cycle of the process shown in the fi gure?

A heat engine operates between a reservoir at 25 C and one at 375 C. What is the maximum effi ciency possible for this engine?

A heat engine is being designed to have a Carnot effi ciency of 65% when operating between two heat reservoirs. (a) If the temperature of the cold reservoir is 20 C, what must be the temperature of the hot reservoir? (b) Can the actual effi ciency of the engine be equal to 65%? Explain.

The work done by an engine equals one-fourth the energy it absorbs from a reservoir. (a) What is its thermal effi ciency? (b) What fraction of the energy absorbed is expelled to the cold reservoir?

A particular engine has a power output of 5.00 kW and an effi ciency of 25.0%. If the engine expels 8 000 J of energy in each cycle, fi nd (a) the energy absorbed in each cycle and (b) the time required to complete each cycle.

One of the most effi cient engines ever built is a coal-fi red steam turbine engine in the Ohio River valley, driving an electric generator as it operates between 1 870 C and 430 C. (a) What is its maximum theoretical effi ciency? (b) Its actual effi ciency is 42.0%. How much mechanical power does the engine deliver if it absorbs 1.40 _ 105 J of energy each second from the hot reservoir?

A gun is a heat engine. In particular, it is an internal combustion piston engine that does not operate in a cycle, but comes apart during its adiabatic expansion process. A certain gun consists of 1.80 kg of iron. It fi res one 2.40-g bullet at 320 m/s with an energy effi ciency of 1.10%. Assume the body of the gun absorbs all the energy exhaust and increases uniformly in temperature for a short time before it loses any energy by heat into the environment. Find its temperature increase.

An engine absorbs 1 700 J from a hot reservoir and expels 1 200 J to a cold reservoir in each cycle. (a) What is the engines effi ciency? (b) How much work is done in each cycle? (c) What is the power output of the engine if each cycle lasts 0.300 s?

A heat pump has a coeffi cient of performance of 3.80 and operates with a power consumption of 7.03 _ 103 W. (This power usage corresponds to that of a 2-ton unit.) (a) How much energy does the heat pump deliver into a home during 8.00 h of continuous operation? (b) How much energy does it extract from the outside air in 8.00 h?

A freezer has a coeffi cient of performance of 6.30. The freezer is advertised as using 457 kW-h/y. (a) On average, how much energy does the freezer use in a single day? (b) On average, how much thermal energy is removed from the freezer each day? (c) What maximum amount of water at 20.0 C could the freezer freeze in a single day? (One kilowatt-hour is an amount of energy equal to running a 1-kW appliance for one hour.)

Suppose an ideal (Carnot) heat pump could be constructed. (a) Using Equation 12.15, obtain an expression for the coeffi cient of performance for such a heat pump in terms of Th and Tc. (b) Would such a heat pump work better if the difference in the operating temperatures were greater or were smaller? (c) Compute the coeffi cient of performance for such a heat pump if the cold reservoir is 50.0 C and indoor temperature is 70.0 C.

In one cycle a heat engine absorbs 500 J from a hightemperature reservoir and expels 300 J to a lowtemperature reservoir. If the effi ciency of this engine is 60% of the effi ciency of a Carnot engine, what is the ratio of the low temperature to the high temperature in the Carnot engine?

A power plant has been proposed that would make use of the temperature gradient in the ocean. The system is to operate between 20.0 C (surface water temperature) and 5.00 C (water temperature at a depth of about 1 km). (a) What is the maximum effi ciency of such a system? (b) If the useful power output of the plant is 75.0 MW, how much energy is absorbed per hour? (c) In view of your answer to part (a), do you think such a system is worthwhile (considering that there is no charge for fuel)?

A nuclear power plant has an electrical power output of 1 000 MW and operates with an effi ciency of 33%. If excess energy is carried away from the plant by a river with a fl ow rate of 1.0 _ 106 kg/s, what is the rise in temperature of the fl owing water?

A heat engine operates in a Carnot cycle between 80.0 C and 350 C. It absorbs 21 000 J of energy per cycle from the hot reservoir. The duration of each cycle is 1.00 s. (a) What is the mechanical power output of this engine? (b) How much energy does it expel in each cycle by heat?

A Styrofoam cup holding 120 g of hot water at 1.00 _ 102 C cools to room temperature, 20.0 C. What is the change in entropy of the room? (Neglect the specifi c heat of the cup and any change in temperature of the room.)

Two 2 000-kg cars, both traveling at 20 m/s, undergo a head-on collision and stick together. Find the change in entropy of the Universe resulting from the collision if the temperature is 23C.

A freezer is used to freeze 1.0 L of water completely into ice. The water and the freezer remain at a constant temperature of T _ 0 C. Determine (a) the change in the entropy of the water and (b) the change in the entropy of the freezer.

What is the change in entropy of 1.00 kg of liquid water at 100 C as it changes to steam at 100 C?

A 70-kg log falls from a height of 25 m into a lake. If the log, the lake, and the air are all at 300 K, fi nd the change in entropy of the Universe during this process.

If you roll a pair of dice, what is the total number of ways in which you can obtain (a) a 12? (b) a 7?

The surface of the Sun is approximately at 5 700 K, and the temperature of the Earths surface is approximately 290 K. What entropy change occurs when 1 000 J of energy is transferred by heat from the Sun to the Earth?

When an aluminum bar is temporarily connected between a hot reservoir at 725 K and a cold reservoir at 310 K, 2.50 kJ of energy is transferred by heat from the hot reservoir to the cold reservoir. In this irreversible process, calculate the change in entropy of (a) the hot reservoir, (b) the cold reservoir, and (c) the Universe, neglecting any change in entropy of the aluminum rod. (d) Mathematically, why did the result for the Universe in part (c) have to be positive?

Prepare a table like Table 12.3 for the following occurrence: You toss four coins into the air simultaneously and record all the possible results of the toss in terms of the numbers of heads and tails that can result. (For example, HHTH and HTHH are two possible ways in which three heads and one tail can be achieved.) (a) On the basis of your table, what is the most probable result of a toss? In terms of entropy, (b) what is the most ordered state, and (c) what is the most disordered?

When a metal bar is temporarily connected between a hot reservoir at Th and a cold reservoir at Tc , the energy transferred by heat from the hot reservoir to the cold reservoir is Qh. In this irreversible process, fi nd expressions for the change in entropy of (a) the hot reservoir, (b) the cold reservoir, and (c) the Universe.

Energetically, 1 lb of fat is equivalent to 1.7 _ 107 J. How much extra weight would you lose each year if you substituted one hour of physics study a day (considered desk work) for one hour of sleep?

A weightlifter has a basal metabolic rate of 80.0 W. As he is working out, his metabolic rate increases by about 650 W. (a) How many hours does it take him to work off a 450-Calorie bagel if he stays in bed all day? (b) How long does it take him if hes working out? (c) Calculate the amount of mechanical work necessary to lift a 120-kg barbell 2.00 m. (d) He drops the barbell to the fl oor and lifts it repeatedly. How many times per minute must he repeat this process to do an amount of mechanical work equivalent to his metabolic rate increase of 650 W during exercise? (e) Could he actually do repetitions at the rate found in part (d) at the given metabolic level? Explain.

Sweating is one of the main mechanisms with which the body dissipates heat. Sweat evaporates with a latent heat of 2 430 kJ/kg at body temperature, and the body can produce as much as 1.5 kg of sweat per hour. If sweating were the only heat dissipation mechanism, what would be the maximum sustainable metabolic rate, in watts, if 80% of the energy used by the body goes into waste heat? ADDITIONAL PROBLEMS

A Carnot engine operates between the temperatures Th _ 100 C and Tc _ 20 C. By what factor does the theoretical effi ciency increase if the temperature of the hot reservoir is increased to 550 C?

A 1 500-kW heat engine operates at 25% effi ciency. The heat energy expelled at the low temperature is absorbed by a stream of water that enters the cooling coils at 20 C. If 60 L fl ows across the coils per second, determine the increase in temperature of the water.

A Carnot engine operates between 100 C and 20 C. How much ice can the engine melt from its exhaust after it has done 5.0 _ 104 J of work?

A substance undergoes the cyclic process shown in Figure P12.61. Work output occurs along path AB while work input is required along path BC, and no work is involved in the constant volume process CA. Energy transfers by heat occur during each process involved in the cycle. (a) What is the work output during process AB? (b) How much work input is required during process BC? (c) What is the net energy input Q during this cycle? FIGURE P12.61 10.0 50.0 A C B V (liters) P (atm) 1.00 5.00

When a gas follows path 123 on the PV diagram in Figure P12.62, 418 J of energy fl ows into the system by heat and _167 J of work is done on the gas. (a) What is the change in the internal energy of the system? (b) How much energy Q fl ows into the system if the gas follows path 143? The work done on the gas along this path is _63.0 J. What net work would be done on or by the system if the system fol- lowed (c) path 12341 and (d) path 14321? (e) What is the change in internal energy of the system in the processes described in parts (c) and (d)?

A 100-kg steel support rod in a building has a length of 2.0 m at a temperature of 20 C. The rod supports a hanging load of 6 000 kg. Find (a) the work done on the rod as the temperature increases to 40 C, (b) the energy Q added to the rod (assume the specifi c heat of steel is the same as that for iron), and (c) the change in internal energy of the rod.

An ideal gas initially at pressure P0, volume V0, and temperature T0 is taken through the cycle described in Figure P12.64. (a) Find the net work done by the gas per cycle in terms of P0 and V0. (b) What is the net energy Q added to the system per cycle? (c) Obtain a numerical value for the net work done per cycle for 1.00 mol of gas initially at 0 C. (Hint: Recall that the work done by the system equals the area under a PV curve.)

One mole of neon gas is heated from 300 K to 420 K at constant pressure. Calculate (a) the energy Q transferred to the gas, (b) the change in the internal energy of the gas, and (c) the work done on the gas. Note that neon has a molar specifi c heat of c _ 20.79 J/mol _ K for a constantpressure process.

Every second at Niagara Falls, approximately 5 000 m3 of water falls a distance of 50.0 m. What is the increase in entropy per second due to the falling water? Assume the mass of the surroundings is so great that its temperature and that of the water stay nearly constant at 20.0 C. Also assume a negligible amount of water evaporates.

A cylinder containing 10.0 moles of a monatomic ideal gas expands from _ to _ along the path shown in Figure P12.67. (a) Find the temperature of the gas at point _ and the temperature at point _. (b) How much work is done by the gas during this expansion? (c) What is the change in internal energy of the gas? (d) Find the energy transferred to the gas by heat in this process.

Two moles of molecular hydrogen (H2) react with 1 mole of molecular oxygen (O2) to produce 2 moles of water (H2O) together with an energy release of 241.8 kJ/mole of water. Suppose a spherical vessel of radius 0.500 m contains 14.4 moles of H2 and 7.2 moles of O2 at 20.0 C. (a) What is the initial pressure in the vessel? (b) What is the initial internal energy of the gas? (c) Suppose a spark ignites the mixture and the gases burn completely into water vapor. How much energy is produced? (d) Find the temperature and pressure of the steam, assuming its an ideal gas. (e) Find the mass of steam and then calculate the steams density. (f) If a small hole were put in the sphere, what would be the initial exhaust velocity of the exhausted steam if spewed out into a vacuum? (Use Bernoullis equation.)

Suppose you spend 30.0 minutes on a stair-climbing machine, climbing at a rate of 90.0 steps per minute, with each step 8.00 inches high. If you weigh 150 lb and the machine reports that 600 kcal have been burned at the end of the workout, what effi ciency is the machine using in obtaining this result? If your actual effi ciency is 0.18, how many kcal did you actually burn?

Hydrothermal vents deep on the ocean fl oor spout water at temperatures as high as 570 C. This temperature is below the boiling point of water because of the immense pressure at that depth. Because the surrounding ocean temperature is at 4.0 C, an organism could use the temperature gradient as a source of energy. (a) Assuming the specifi c heat of water under these conditions is 1.0 cal/g _ C, how much energy is released when 1.0 liter of water is cooled from 570 C to 4.0 C? (b) What is the maximum usable energy an organism can extract from this energy source? (Assume the organism has some internal type of heat engine acting between the two temperature extremes.) (c) Water from these vents contains hydrogen sulfi de (H2S) at a concentration of 0.90 mmole/liter. Oxidation of 1.0 mole of H2S produces 310 kJ of energy. How much energy is available through H2S oxidation of 1.0 L of water?

An electrical power plant has an overall effi ciency of 15%. The plant is to deliver 150 MW of electrical power to a city, and its turbines use coal as fuel. The burning coal produces steam at 190 C, which drives the turbines. The steam is condensed into water at 25 C by passing through coils that are in contact with river water. (a) How many metric tons of coal does the plant consume each day (1 metric ton _ 1 _ 103 kg)? (b) What is the total cost of the fuel per year if the delivery price is $8 per metric ton? (c) If the river water is delivered at 20 C, at what minimum rate must it fl ow over the cooling coils so that its temperature doesnt exceed 25 C? (Note: The heat of combustion of coal is 7.8 _ 103 cal/g.)