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**1.** In question 1, we consider processes similar to Process A from the tutorial, with a block with heat capacity 400 J/K and initial temperature 280 K and a second block with heat capacity 200 J/K and initial temperature 340 K.

**A.** In process B, the 280 K block and 340 K block change in temperature, but in the opposite direction as in process A. In other works, the temperature of the 280 K block decreases to 260 K and the 340 K block increases to 380 K. The blocks are still thermally isolated from all other objects.

1. Is process B allowed by the first law of thermodynamics? Explain your reasoning.

2. What is the total change in entropy of the two-block system during process B?

**B.** In process C, both blocks begin at 300 K but their temperatures diverge so that the block with heat

capacity 400 J/K ends up at a temperature of 280 K and the other ends up at 340 K. (Note that this

process is the reverse of process A).

1. Is process C allowed by the first law of thermodynamics? Explain your reasoning.

2. Using your result from part A.5, find the change in entropy for each block and for the two block system during process C.

**C.** The following questions refer to processes A (from the tutorial), B, and C.

1. For those processes that you would expect to observe, was the total change in entropy of all systems involved greater than, less than, or equal to zero?

2. For those processes that you would not expect to observe, was the total change in entropy of all systems involved greater than, less than, or equal to zero?

**2.** Consider a macroscopic system of two blocks that are in thermal contact. The two-block system is isolated from the rest of the universe. Initially, a hotter block is at a temperature TH and a colder block is at a temperature TC. In the final state of the system, the two blocks are at the same intermediate temperature TI.

**A.** Compare the following quantities for the initial state and final state: Entropy for the block that starts at TH

Sf > Si Sf < Si Si = Sf not enough information

Entropy for the block that starts at TL

Sf > Si Sf < Si Si = Sf not enough information

Combined entropy for the two block system

Sf > Si Sf < Si Si = Sf not enough information

**B.** Consider the following statement:

*“When the blocks approach equilibrium, they move to a final state that is more natural, so their level*

*of order increases.”*

Do you agree with this statement?

Does this statement agree with the second law of thermodynamics?

**3.** An ice cube with a mass of 30.0 g is dropped into a beaker of water. The initial temperature of the ice cube is 0° C and the initial temperature of the water in the beaker is 20° C. The heat capacity of the water in the beaker is 2000 J/K. The latent heat of fusion for water is 333 J/g. Assume that the system consisting of the beaker and the cube does not thermally interact with its surroundings.

A. Determine the equilibrium temperature of the system.

B. Find the changes in entropy for the following processes and carefully specify the system (or subsystem) for which you found ΔS.

a. the melting of the ice cube: (Hint: Does the temperature of the ice change during this process?)

b. the cooling of the water as the ice cube is melting:

c. the heating of the melted ice to its final temperature:

d. the cooling of the warm water to its final temperature:

**C**. Find the total change in entropy during the process:

**D**. Would you expect the reverse of this process (i.e., 30 g of ice forms spontaneously from a beaker of water at the final temperature) to occur? Is the reverse of this process forbidden by the first or second law of thermodynamics?

HW file is also being attached below along with the tutorial paper too.

Physics 535
HW: ENTROPY
Name
1. In question 1, we consider processes similar to Process A from the tutorial, with a block with heat
capacity 400 J/K and initial temperature 280 K and a second block with heat capacity 200 J/K and
initial temperature 340 K.
A. In process B, the 280 K block and 340 K block change in temperature, but in the opposite direction as
in process A. In other works, the temperature of the 280 K block decreases to 260 K and the 340 K
block increases to 380 K. The blocks are still thermally isolated from all other objects.
1. Is process B allowed by the first law of thermodynamics? Explain your reasoning.
2. What is the total change in entropy of the two-block system during process B?
B. In process C, both blocks begin at 300 K but their temperatures diverge so that the block with heat
capacity 400 J/K ends up at a temperature of 280 K and the other ends up at 340 K. (Note that this
process is the reverse of process A).
1. Is process C allowed by the first law of thermodynamics? Explain your reasoning.
2. Using your result from part A.5, find the change in entropy for each block and for the two-block
system during process C.
C. The following questions refer to processes A (from the tutorial), B, and C.
1. For those processes that you would expect to observe, was the total change in entropy of all
systems involved greater than, less than, or equal to zero?
2. For those processes that you would not expect to observe, was the total change in entropy of all
systems involved greater than, less than, or equal to zero?
Adapted with permission from Michael Loverude
ENTROPY
Physics 535
2. Consider a macroscopic system of two blocks that are in thermal contact. The two-block system is
isolated from the rest of the universe. Initially, a hotter block is at a temperature TH and a colder block is
at a temperature TC. In the final state of the system, the two blocks are at the same intermediate
temperature TI.
A. Compare the following quantities for the initial state and final state:
Entropy for the block that starts at TH
Sf > Si
Sf < Si
Si = Sf
not enough information
Entropy for the block that starts at TL
Sf > Si
Sf < Si
Si = Sf
not enough information
Combined entropy for the two block system
Sf > Si
Sf < Si
Si = Sf
not enough information
B. Consider the following statement:
“When the blocks approach equilibrium, they move to a final state that is more natural, so their level
of order increases.”
Do you agree with this statement?
Does this statement agree with the second law of thermodynamics?
Adapted with permission from Michael Loverude
Physics 535
ENTROPY
3. An ice cube with a mass of 30.0 g is dropped into a beaker of water. The initial temperature of the ice
cube is 0° C and the initial temperature of the water in the beaker is 20° C. The heat capacity of the water
in the beaker is 2000 J/K. The latent heat of fusion for water is 333 J/g. Assume that the system
consisting of the beaker and the cube does not thermally interact with its surroundings.
A. Determine the equilibrium temperature of the system.
B. Find the changes in entropy for the following processes and carefully specify the system (or
subsystem) for which you found ΔS.
a. the melting of the ice cube: (Hint: Does the temperature of the ice change during this process?)
b. the cooling of the water as the ice cube is melting:
c. the heating of the melted ice to its final temperature:
d. the cooling of the warm water to its final temperature:
C. Find the total change in entropy during the process:
D. Would you expect the reverse of this process (i.e., 30 g of ice forms spontaneously from a beaker of
water at the final temperature) to occur? Is the reverse of this process forbidden by the first or second
law of thermodynamics?
Adapted with permission from Michael Loverude
ENTROPY
Physics 535
Consider two blocks. The initial temperature of block 1 is 280 K and the initial temperature of block 2 is
340 K. The heat capacities of blocks 1 and 2 are 400 J/K and 200 J/K, respectively.
A. The two blocks are placed in thermal contact with one another but are perfectly insulated from the
remainder of their surroundings. We will call the process that begins when the blocks are brought in
contact with one another process A.
1. Determine the final temperature of the two blocks.
2. Determine the heat transfer to each block during process A (including sign).
In lecture we articulated the relationship dS = dQ / T for an infinitesimal reversible change. Since entropy
is a state function, we can calculate the change in entropy for any process by imagining reversible
processes that have the same initial and final state as the process. For Process A, we can imagine placing
block 1 in contact with a series of thermal reservoirs at temperatures T1, T1 + δT, T1 + 2δT, . . . Tfinal and
placing block 2 in contact with a series of thermal reservoirs at temperatures T2, T1 - δT, T1 - 2δT, . . . Tfinal.
Thus we replace dQ by CP dT and integrate to find the change in entropy.
3.
Write an expression for ΔS by integrating dS = dQ / T, given that dQ = CP dT.
4. Determine the change in entropy during process A (including sign)
•
for block 1:
• for block 2:
5. Is process A reversible? Explain.
1
Adapted with permission from Michael Loverude
• for the system
Physics 310
ENTROPY
In the tutorial homework, you will consider two related processes involving this pair of blocks. Process B
has the same starting point as process A, but the temperatures of the blocks diverge, so that the cold block
gets colder and the hot block gets hotter. Process C is the reverse of Process A, in which two blocks start
at the same temperature but one spontaneously cools and the other warms up.
B. In process B, the 280 K block and 340 K block change in temperature, but in the opposite direction as
in process A. In other works, the temperature of the 280 K block decreases to 260 K and the 340 K
block increases to 380 K. The blocks are still thermally isolated from all other objects.
1. Is process B allowed by the first law of thermodynamics? Explain your reasoning.
2. What is the total change in entropy of the two-block system during process B?
C. In process C, both blocks begin at 300 K but their temperatures diverge so that the block with heat
capacity 400 J/K ends up at a temperature of 280 K and the other ends up at 340 K. (Note that this
process is the reverse of process A).
1. Is process C allowed by the first law of thermodynamics? Explain your reasoning.
2. Using your result from part A.5, find the change in entropy for each block and for the two-block
system during process C.
D. The following questions refer to processes A, B, and C.
1. For those processes that you would expect to observe, was the total change in entropy of all
systems involved greater than, less than, or equal to zero?
2. For those processes that you would not expect to observe, was the total change in entropy of all
systems involved greater than, less than, or equal to zero?
2
Adapted with permission from Michael Loverude
...

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solution attached

QUESTION 1:

A)

1. The process B is allowed by the first law of thermodynamics because

work done by block A work done by block B

400 J / K 280 K 260 K 200 J / K 380 K 340 K

8000 J 8000 J

2. The total change in entropy of the two-block system during process is calculated by

T

T

S C A ln A1 CB ln B1

TA2

TB 2

260

380

400 ln

200 ln

280

340

7.40

B)

1. Process C is not allowed by the first law of thermodynamics since

work done by block C =

= 400 J / K 340 K 280 K

24000 J

which is not the same work done of 8000 J as in the answer in part A.

2. The total change in entropy of each block is calculated by

For block 1:

T

280 K

S1 C ln 1 f 400 J / K ln

27.60

300K

T1i

For block 2:

T

340 K

S1 C ln 1 f 400 J / K ln

50.07

300 K

T1i

The two-block system during process is calculated by

S S1 S2 27.60 50.07 22.47

C)

1. The total change in entropy of all systems involved was less than zero as ...

Review

Anonymous

Excellent job

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