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
Carnotâs 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 KelvinâPlanck 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.
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
Carnotâs 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 KelvinâPlanck 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.
