# Homework Help: Thermally Challenged Help!

1. Dec 8, 2004

### PhysicsNovice

Great news. I am on my last on-line physics module before the Holiday season comes along. I have posted and answered my self-assessment questions (answers appear with *asterisk). Again, please let me know the ones I answered correctly on and the ones I missed (I think there are many because this material was difficult) give a gentle push in the right direction (i.e. a formula, hint,). I will then provide my thought process on why I answered the way I did. Thanks to everyone who has helped me in the past three months. Happy Holiday!

1. The second law of thermodynamics says that:
a. the energy of an isolated system is conserved.
b. it is impossible to build a heat engine that can do mechanical work by extracting thermal energy that does not also exhaust heat to the surroundings.
c. it is impossible to reach the absolute zero of temperature.
d. it is impossible to build a heat engine that does more mechanical work than the thermal energy it consumes.*

2. Many people have tried to build perpetual-motion machines. Our study of physics tells us that perpetual-motion machines are:
a. theoretically possible, but difficult to build.
b. theoretically possible if they do not violate the first law of thermodynamics.
c. theoretically possible, but would be very inefficient.
d. not possible to build.*

3. The efficiency of an ideal heat engine can be improved by __________ the input temperature and __________ the exhaust temperature.
a. increasing ... increasing
b. increasing ... decreasing*
c. decreasing ... increasing
d. decreasing ... decreasing

4. A heat engine takes in 600 J of energy at 1000 K and exhausts 300 J at 400 K. What is the maximum theoretical efficiency of this engine?
a. 40%
b. 50%*
c. 60%
d. 80%

5. An engine has an efficiency of 40%. How much energy must be extracted to do 900 J of work?
a. 360 J
b. 900 J
c. 2250 J
d. 3600 J*

6. The second law of thermodynamics says that:
a. the energy of an isolated system is conserved.
b. it is impossible to build a refrigerator that can transfer heat from a lower temperature region to a higher temperature region without expending mechanical work.
c. it is impossible to reach the absolute zero of temperature.
d. it is impossible to build a refrigerator that exhausts more heat than the mechanical work required to operate it.*

7. An air-conditioner mechanic is testing a unit by running it on the workbench in an isolated room? What happens to the temperature of the room?
a. It increases.*
b. It decreases.
c. It stays the same.

8. The second law of thermodynamics:
a. says that it is impossible to reach the absolute zero of temperature.
b. says that the entropy of a system tends to increase.*
c. is the basis for the definition of temperature.
d. is the basis for the definition of internal energy.

9. In which of the systems listed below is the entropy decreasing?
a. A gas is cooled.*
b. A plate is shattered.
c. An egg is scrambled.
d. A drop of dye diffuses in a cup of water.

10. A cold piece of metal is dropped into an insulated container of hot water. After the system has reach an equilibrium temperature, the:
a. entropy of the metal has decreased.
b. entropy of the water has increased.
c. net change in entropy of the system is zero.*
d. entropy of the system has increased.

2. Dec 8, 2004

### dextercioby

On a first look,questions 5 and 10 need to be revised.

3. Dec 8, 2004

### Palindrom

Maybe it's just me, but I'd say the first one needs revising as well.

4. Dec 8, 2004

### dextercioby

No,the answer to the first is in perfect agreement with both the second principle (any formulation,since they're logically equivalent) and with the definition of "\eta" as the ratio between the work made and the heat needed to do that worh."\eta" cannot ecceed 1.It can't even be 1.
So "d)" makes a good choise of answer.

5. Dec 9, 2004

### Clausius2

I am not agree at questions:

4) I would say 60%:

$$\eta_{carnot}=1-T_c/T_h$$ is the maximum theoretical efficiency of any heat engine working between those temperatures.

5) I would say c)

10) I would say d)

6. Dec 9, 2004

### Staff: Mentor

regarding question 1

I would say that answer d is a statement of the first law of thermodynamics (energy conservation), not the second. Loosely speaking, it says: You can't get something for nothing. The second law goes further: You can't break even. Answer b is the best match.

7. Dec 9, 2004

### Calculex

The answer to question 6 is wrong. Heat pumps do 6d) all the time. The correct answer is b).

I agree with others that the answers to 1, 4, 5 and 10 are wrong and the correct answers are: 1b, 4c, 5c, (although I am confused by the word 'extracted'), and 10d.

With respect to 5, Efficiency is the ratio of work done to the amount of heat energy input. So I am assuming that 'extracted' refers to heat extracted from an external source to be used as input heat for the engine.

8. Dec 10, 2004

### Clausius2

I don't agree with that, Doc. Imagine a heat engine that extracts a heat Q_h from the chemical reaction of combustion and produces a work W. The first principle states:

$$W=Q_h$$ Ok?

Well, that is absolutely wrong. And we can afirm that due to the second principle which doesn't allow that energy flux. There must be a waste of energy at the exhaust, in order to satisfy the second principle:

$$W=Q_h-Q_c$$ as the 1st and 2nd principle yield.

What do you think about that?

9. Dec 10, 2004

### Staff: Mentor

I think you are reading way too much into this simple question!

Choice d said:
d. it is impossible to build a heat engine that does more mechanical work than the thermal energy it consumes.*​
To me, that is a statement of conservation of energy or the first law. As you yourself point out, the 2nd law says more than that. So, is choice "d" a good statement of the 2nd law? No.

10. Dec 10, 2004

### Clausius2

I keep on not agreeing with you.

It is an statement of the first principle? Yes.

It is an statement of the second principle? Yes. Because there are several statements of the first principle that do not match with the second one. In particular, the option d) is the official statement of the 2nd principle and was made by Kelvin or Planck (i don't remember that). In all thermal physics books the second principle is stated in various forms, and one of them is the option d).

MORE: think of that. Suppose you have a time travel machine and return to the age when 2nd principle was not discovered. You are planning to invent a heat engine. Applying the first principle you say:

$$W=Q_{combustion}$$

You built the heat engine, but when you're testing it you realize that balance doesn't fit the reality. Then you reformulate the 1st principle and go beyond:

" it is impossible to build a heat engine that does more mechanical work than the thermal energy it consumes"

Congratulations!! You have discovered the 2nd principle!! :rofl:

Last edited: Dec 10, 2004
11. Dec 10, 2004

### Staff: Mentor

A heat heat engine that does an amount of work exactly equal to the thermal energy it consumes would satisfy option "d" (and the 1st law) but clearly violates the 2nd law. On the other hand, option "b":
"b. it is impossible to build a heat engine that can do mechanical work by extracting thermal energy that does not also exhaust heat to the surroundings."​
seems to be a good statement of the 2nd law.

12. Dec 10, 2004

### Clausius2

I see where are you getting at. Hmmmm....Now I must agree with you. Yes Doc, you seem to be right. Excuse me for my stubbornness. I usually don't read the rest of the options in those tests...