Heat Engines and the Second Law of Thermodynamics Answers to Questions Q1

coralmonkeyΜηχανική

27 Οκτ 2013 (πριν από 3 χρόνια και 7 μήνες)

44 εμφανίσεις

31

11

Heat Engines and the Second Law of Thermodynamics


Answers to Questions


Q1


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
ion
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.

Q2

No. They are not taking in heat energy. They convert mechanical energy into work.

Q3


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.

Q4

No. In one cycle the heat rejected must be less than the heat admitted by the net amount of work done.

Q5


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.

Q6


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.

Q7


Such a heat engine would convert all heat input into work, which would violate the Second Law of
Thermodynamics.

Q8

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.

Q9

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.

Q10


No. That would violate the Second Law of Thermodynamics by allowing complete conversion of heat
energy input into

work.

Q11


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.

Q12

No. There are many irreversible processes taking place in an automobile
engine including the explosive
burning of the gasoline
-
air mixture.

Q13

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).

Q14

Lower the temperature of the low tem
perature reservoir since the efficiency increases as the inverse of the
high temperature.

Q15

A heat pump is a heat engine that removes heat from a cool environment and transfers it to a warmer
environment.

Q16

Yes. Work is done to remove heat from the coo
l environment reservoir and deposit it in the high
temperature reservoir.

Q17

The heat is most likely removed from the already cool outdoors. This would be the cool heat reservoir.

Q18


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.

Q19

Yes. This is what a refrigerator does. It doesn't violate the Second Law because work is performed to
accomplish it.

Q20

Work must be perform
ed in order to remove heat from the cool reservoir and move it to the hot reservoir.

Q21


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.

Q22



This diagram is correct. More heat is transferred to the hot reservoir than is taken in from the cold one, with
work being done.

Q23

The shuffled deck of cards

has the higher entropy. It represents a more disordered system.

Q24

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.

Q25


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.

32

Q26


A coal
-
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
-
burning plant.

Q27


Both plants generate steam, which drives the turbine to generate electricity.

Q28


High
-
grade heat (500

C and higher) has a higher potential for work production than does low
-
grade heat

(100

C and below).


Q29


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
mechanical ene
rgy can be lower than a gasoline engine.

Q30


Heat obtained from a flat plate collector is best used for space heating because it is low
-
grade (no more
than 100

C) heat and therefore has a low potential for work production.

Q31


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
running.

Q32

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
yer.

Q33


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


E1


40%

E2


1600 J

E3


a.

300 J


b.

33 %

E4

a.

240 J


b.

360 J

E5


a.

900 J


b.

44.4 %

E6


46 %

E7


59 %

E8


a.

33 %


b.

455 J

E9

450 J

E10


12 J

E11

500 W

E12

41.8 %

E13

No. The Carnot efficiency for this plant is 4%.

E14

10.2 %





Answers to Synthesis Probl
ems


SP1

a.

37.5 MJ


b.

112.5 MJ


c.

The work is used to overcome friction.


d.

Cold day because the engine is able to get a greater compression of the intake air.

SP2

a.

45.3 %


b.

66.3 J


c.

36.3 J


d.

Zero

SP3



a.

6.7 %


b.

13.4 J


c.

186.6 J


d.

13.9

33


e.

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.

SP4

We leave this as an exercise in critical thinking.

SP5


a.

44.4 %


b.

35.5 %


c.

1 x 10
5

kW h


d.

2.82 x 10
5

kW h


e.

165.5 barrels of oil