Exam #4 Spring 2000

1. A heat engine uses an ideal gas as its working “fluid” with a constant volume heat capacity cv = 20.71 J/mol/K. The gas cycle starts by compression (1 to 2) at constant pressure, then heating (2 to 3) at constant volume, and then expansion (3 to1) at a constant temperature as shown in the diagram.
(A) What amount of heat does this engine exhaust during one cycle?
Ans:{3.52 kJ}
(B) What is the maximum possible thermal efficiency that this could perform if where a Carnot engine?
Ans:{75.0%}
(C) What is the net work done by this engine in one cycle?
Ans:{855 J}
2. A heat engine produces 46.0 kW of useful power when operating from a heat supply at 180oC. The engine has thermal efficiency of 19.0% and maximum possible thermal efficiency of 32.0%.
(A) How much heat energy does this engine absorb from its heat supply in one hour ?
Ans:{872 MJ}
(B) At what temperature does this engine exhaust its waste energy?
Ans:{308 K}
(C) What is the change in entropy per second of a large heat reservoir into which this engine exhausts its heat when the engine is operating at efficiency 19.0%?
Ans:{636J/K}
3. A reversible heat pump with a coefficient of performance of 12.0 is used to boil 260 grams of water initially at 40.0oC until it is steam at 100oC.
(A) How much work does the heat pump do to accomplish this task?
Ans:{54.4kJ or 13.0 kcal}
(B) What is the change in entropy of water?
Ans:{422 cal/K or 1.76 kJ/K}}
(C) If the heat pump draws its energy from a large heat reservoir, what must the temperature of this heat reservoir be if the heat pump is reversible?
Ans:{340 K}
4. An ideal gas is allowed to expand reversibly from some initial state to the same final volume Vf by three different processes – isothermal, adiabatic, and isobaric expansion.
(A) Sketch the three processes on the PV diagram and label them. State which process does the least amount of work. Sketch this process’s work on the PV diagram.
Ans:{DQ = 0}

(B) In which process is the change in internal energy the greatest? Using the equations for internal energy of the different processes explain why.
Ans:{DP = 0 since DU = m cV(Tf – T i) and T f is the largest for DP = 0 process.}
(C) In which process is the change in entropy of the ideal gas the greatest? Using the equations for internal energy of the different processes explain why.
Ans:{DP = 0 since cP > R and
DS T = nR ln(Vf/Vo),
DSP = ncP ln(Tf/To) = ncP ln(Vf/Vo) since Vo/Vf = To/Tf, for DP = 0
and DSQ = 0}

Exam #4 W2000

1. A heat engine produces 46.0 kW of useful work when operating from a heat supply at 180oC. The engine exhausts 380 kilocalories per minute of heat into a stream at 14.0oC

2. A refrigerator removes heat from 190 grams of water at 0.00 oC until the water is turned into ice at 0.00 oC. The exhaust heat is rejected into the air at 23.0oC.

3. The working fluid in a heat engine is 1.75 moles of an ideal gas with cp = 29.02 J/mol/K and cv = 20.71 J/mol/K. The heat engine follows the cycle shown.
(A) How much heat does this heat engine take in during one cycle?
Ans:{ 3.23 kcal}
(B) What is the net work done by this engine during one cycle?
Ans:{1.69 kJ}
(C) What is the change in entropy of the working fluid when it exhausts heat?
Ans:{-30.5 J/K}

TA = 656 K, TB = 516 K, TC = 283 K
VA = VC = 4.5 liters, VB = 8.20 liters
PA = 2120 kPa, PB = PC = 915 kPa

4. A reversible heat pump is use to transfer heat from a low temperature reservoir at 25.0oC to an insulated 5.80 m3 rigid tank containing 7.90 moles of an ideal gas with cp = 20.80 cal/mol/K and cv = 12.49 cal/mol/K. Initially the temperature of the ideal gas is 35.0oC