Heat Engines and the Second Law of Thermodynamics
Answers to Questions
The heat engines are
a. and c. A heat engine converts thermal energy into work, always exhausting some of
the thermal energy at a lower tempera
ture. The automobile engine
is an example of an internal combust
engine that develops heat internally rather than extracting it from an external source. The steam turbine is an
example of an external combustion engine, obtaining the energy to produce the superheated steam from
heating outside of the turbine. The electric motor converts electrical energy into work.
No. They are not taking in heat energy. They convert mechanical energy into work.
A heat engine operates in a cycle. When the working substance has been rest
ored to its initial state, it must
again have the same internal energy.
No. In one cycle the heat rejected must be less than the heat admitted by the net amount of work done.
No. An efficiency greater than 1.0 means that more energy is output than
is input to the heat engine, which
would violate the First Law of Thermodynamics.
The First Law. Since in one cycle the internal energy of the working substance in the heat engine will be
unchanged, for the cycle as a whole the net heat absorbed must
be equal to net work output. The net heat
absorbed is the difference between the heat absorbed and heat rejected per cycle.
Such a heat engine would convert all heat input into work, which would violate the Second Law of
No. The h
ypothetical engine is extracting heat from the high temperature reservoir, exhausting an equal
amount of heat into the low temperature reservoir and also performing work as a result of both these
operations. Exhausting heat is dissipative. It does not resu
lt in work. Also work must be less than the
amount of energy drain from the high temperature reservoir.
No. This hypothetical heat engine extracts heat from a single source, performs work and puts the remaining
heat energy back in the original source o
f heat. The net effect is to extract heat from a single source and
convert it all to work, which is a violation of Kelvin's statement.
No. That would violate the Second Law of Thermodynamics by allowing complete conversion of heat
energy input into
The Carnot engine was invented to be the ideal. The concept of reversibility is a key factor here. If it operated
irreversibly it would no longer be an ideal process.
No. There are many irreversible processes taking place in an automobile
engine including the explosive
burning of the gasoline
The engine operating between 400 K and 300 K has the higher efficiency (.25 compared to .15 for the
engine operating between 400 C and 300 C).
Lower the temperature of the low tem
perature reservoir since the efficiency increases as the inverse of the
A heat pump is a heat engine that removes heat from a cool environment and transfers it to a warmer
Yes. Work is done to remove heat from the coo
l environment reservoir and deposit it in the high
The heat is most likely removed from the already cool outdoors. This would be the cool heat reservoir.
No. This will heat the room. The heat rejected by the refrigerato
r exceeds the heat removed from the inside
of the refrigerator by the work done in operating the appliance.
Yes. This is what a refrigerator does. It doesn't violate the Second Law because work is performed to
Work must be perform
ed in order to remove heat from the cool reservoir and move it to the hot reservoir.
This diagrams an engine that violates the First Law of Thermodynamics. Work is being done to transfer heat
from the cooler reservoir to the hotter reservoir. Howeve
r, more heat is being withdrawn and more work is
being done than is being transferred.
This diagram is correct. More heat is transferred to the hot reservoir than is taken in from the cold one, with
work being done.
The shuffled deck of cards
has the higher entropy. It represents a more disordered system.
Yes. The entropy of the universe increases. Air is the conducting medium for the transfer of heat energy
from the warmer environment (the cup of coffee) to the cooler environment (the a
tmosphere). The random
collisions between air molecules results in the dissipation of the heat among other air molecules resulting,
finally, in a more disordered state.
No. Since it requires energy from some other source. The increase of entropy of t
his source will always be
greater than the loss of entropy of the cooled substance.
fired power plant normally has a much higher thermal efficiency than a geothermal power plant. The
exhaust temperatures are comparable for the two but the hi
gh temperature input is much higher for the coal
Both plants generate steam, which drives the turbine to generate electricity.
grade heat (500
C and higher) has a higher potential for work production than does low
C and below).
Even though the electric motor is very efficient, the power plant that produces the electrical energy is not
highly efficient. Thus, the overall efficiency of producing the electrical power and then converting it to
rgy can be lower than a gasoline engine.
Heat obtained from a flat plate collector is best used for space heating because it is low
grade (no more
C) heat and therefore has a low potential for work production.
No. A perpetual motion ma
chine, once started, would require no additional energy to keep going. The
automobile engine requires continuous input of gasoline that is burned explosively to keep the engine
This power plant is not a perpetual motion machine. The upper and
lower layers are sufficiently separated
to be essentially different reservoirs. As long as natural processes are able to maintain the temperature
differential, it is very unlikely the plant would be able to effectively modify the temperatures of either la
This device violates the Second Law of Thermodynamics because its net effect would be the complete
conversion of heat to work. It is a perpetual motion machine of the second kind.
Answers to Exercises
No. The Carnot efficiency for this plant is 4%.
Answers to Synthesis Probl
The work is used to overcome friction.
Cold day because the engine is able to get a greater compression of the intake air.
Yes. The temperature is in the moderate range for which a real heat pump can provide more heat
energy to the home than is required to run the pump.
We leave this as an exercise in critical thinking.
1 x 10
2.82 x 10
165.5 barrels of oil