PHYS 157 Lecture Notes - Lecture 17: Thermodynamic Cycle

A. Consider two arbitrary heat engines. Engine A hasanefficiency of 60%. Engine B absorbs the same amount ofheat from theheat reservoir as Engine A; however, it exhauststwice as much heatto the cold reservoir as Engine A. Findthe efficiency of EngineB.

B. Consider a nonreversible heat engine that operatesbetweentemperatures T_h and T_c, whereT_c =1/3 T_h. The engine absorbs anamount of heatQ_h from the heat reservoir in order to doan amount ofwork W.

1) If the engine discards an amount of heat Q_c= 3/5Q_h to the cold reservoir, determine the efficiencyofthis engine.

2) How much work, in terms of Q_h, would beavailableto a Carnot heat engine operating between the same twotemperatures?What would the efficiency of this Carnot enginebe?

C. A freezer with a coefficient of performance of 4 isused toconvert 2kg of water to ice in one hour. The waterstarts at atemperature of 20°C, and the ice that is producedis cooled to atemperature of -5°C.

1) How much heat must be removed from the water for thisprocessto occur?

2) How much electrical energy does the freezer use duringthishour of operation?

3) How much heat is discarded into the room that housesthefreezer?

A. Consider two arbitrary heat engines. Engine A hasanefficiency of 60%. Engine B absorbs the same amount ofheat from theheat reservoir as Engine A; however, it exhauststwice as much heatto the cold reservoir as Engine A. Findthe efficiency of EngineB.

B. Consider a nonreversible heat engine that operatesbetweentemperatures T_h and T_c, whereT_c =1/3 T_h. The engine absorbs anamount of heatQ_h from the heat reservoir in order to doan amount ofwork W.

1) If the engine discards an amount of heat Q_c= 3/5Q_h to the cold reservoir, determine the efficiencyofthis engine.

2) How much work, in terms of Q_h, would beavailableto a Carnot heat engine operating between the same twotemperatures?What would the efficiency of this Carnot enginebe?

C. A freezer with a coefficient of performance of 4 isused toconvert 2kg of water to ice in one hour. The waterstarts at atemperature of 20°C, and the ice that is producedis cooled to atemperature of -5°C.

1) How much heat must be removed from the water for thisprocessto occur?

2) How much electrical energy does the freezer use duringthishour of operation?

3) How much heat is discarded into the room that housesthefreezer?

A firebox is at 750 K, and the ambient temperature is
300 K. The efficiency of a Carnot engine doing 150 J of work
as it transports energy between these constant- temperature
baths is 60.0%. The Carnot engine must take in energy
150 J/0.600 5 250 J from the hot reservoir and must put
out 100 J of energy by heat into the environment. To follow
Carnot’s reasoning, suppose some other heat engine
S could have an efficiency of 70.0%. (a) Find the energy
input and exhaust energy output of engine S as it does 150 J
of work. (b) Let engine S operate as in part (a) and run the
Carnot engine in reverse between the same reservoirs. The
output work of engine S is the input work for the Carnot
refrigerator. Find the total energy transferred to or from
the firebox and the total energy transferred to or from the
environment as both engines operate together. (c) Explain
how the results of parts (a) and (b) show that the Clausius
statement of the second law of thermodynamics is violated.
(d) Find the energy input and work output of engine S as it
puts out exhaust energy of 100 J. Let engine S operate as in
part (c) and contribute 150 J of its work output to running theCarnot engine in reverse. Find (e) the total energy the
firebox puts out as both engines operate together, (f) the
total work output, and (g) the total energy transferred to
the environment. (h) Explain how the results show that
the Kelvin–Planck statement of the second law is violated.
Therefore, our assumption about the efficiency of engine S
must be false. (i) Let the engines operate together through
one cycle as in part (d). Find the change in entropy of the
Universe. (j) Explain how the result of part (i) shows that
the entropy statement of the second law is violated.