Lesson test: Irreversibility, the Third Law, and what entropy counts

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Irreversibility, the Third Law, and what entropy counts

1.[2p]
A gas expands freely into an evacuated vessel inside rigid insulated walls. Which set of values is correct?

$Q = 0$ , $W = 0$ , $Δ U = 0$ , $Δ S > 0$

Correct

$Q = 0$ , $W > 0$ , $Δ U < 0$ , $Δ S > 0$

The answer is: $Q = 0$, $W = 0$, $\Delta U = 0$, $\Delta S > 0$

$Q > 0$ , $W = 0$ , $Δ U > 0$ , $Δ S > 0$

The answer is: $Q = 0$, $W = 0$, $\Delta U = 0$, $\Delta S > 0$

$Q = 0$ , $W = 0$ , $Δ U = 0$ , $Δ S = 0$

The answer is: $Q = 0$, $W = 0$, $\Delta U = 0$, $\Delta S > 0$

2.[3p]
Two moles of an ideal gas expand freely from $5$ litres to $15$ litres inside rigid insulated walls. What entropy is generated, in J K⁻¹?

CorrectNot quite: 18.27

3.[3p]
$500$ J of heat leaks from a reservoir at $400$ K into one at $250$ K, and the surroundings are at $250$ K. By Gouy-Stodola, how much work capacity is destroyed, in joules?

CorrectNot quite: 187.5

4.[1p]
Four distinguishable particles are spread between the two halves of a box, giving $16$ microstates in all. How many of them put exactly three particles on the left?

Correct

The answer is: 4

5.[3p]
Why must entropy be the logarithm of the multiplicity rather than some other function of it?

Entropies of independent systems add while their multiplicities multiply

Correct

Multiplicities are too large to write down otherwise

The answer is: Entropies of independent systems add while their multiplicities multiply

The logarithm keeps entropy positive at all temperatures

The answer is: Entropies of independent systems add while their multiplicities multiply

It makes the units come out as joules per kelvin

The answer is: Entropies of independent systems add while their multiplicities multiply

6.[2p]
Counting microstates gives a different entropy change for the free expansion than Clausius's $δ Q_{r e v} / T$ does.

True

The answer is: False

False

Correct

7.[3p]
Which statements about the Third Law are correct?

Select all that apply

Planck's form says the entropy of a perfect crystal tends to zero as $T \to 0$

Correct

It allows absolute entropies to be tabulated rather than only differences

Correct

Ice keeps about $3.4$ J K⁻¹ mol⁻¹ of residual entropy, close to Pauling's predicted $R \ln (3 / 2)$

Correct

It guarantees that absolute zero is reachable given enough cooling stages

The answer is: Planck's form says the entropy of a perfect crystal tends to zero as $T \to 0$, It allows absolute entropies to be tabulated rather than only differences, Ice keeps about $3.4$ J K⁻¹ mol⁻¹ of residual entropy, close to Pauling's predicted $R\ln(3/2)$

8.[2p]
Put these cooling methods in order of the lowest temperature they reach, warmest first.

Adiabatic demagnetisation of a paramagnetic salt, 1933
Nuclear demagnetisation of rhodium, 1999
A dilution refrigerator
Liquid helium at atmospheric pressure

Show the answer

a, b, c, d

9.[2p]
Match each process to the entropy it generates.

One mole of ideal gas expanding freely to twice its volume
One mole each of two gases mixing from equal halves into the whole
$1000$ J crossing from a reservoir at $500$ K to one at $300$ K
Any process run reversibly

$1.33$ J K⁻¹
zero
$R \ln 2$
$2 R \ln 2$

Show the answer

One mole of ideal gas expanding freely to twice its volume: $R \ln 2$ One mole each of two gases mixing from equal halves into the whole: $2 R \ln 2$ $1000$ J crossing from a reservoir at $500$ K to one at $300$ K: $1.33$ J K⁻¹ Any process run reversibly: zero

1.[2p] A gas expands freely into an evacuated vessel inside rigid insulated walls. Which set of values is correct?

2.[3p] Two moles of an ideal gas expand freely from 5 litres to 15 litres inside rigid insulated walls. What entropy is generated, in J K⁻¹?

3.[3p] 500 J of heat leaks from a reservoir at 400 K into one at 250 K, and the surroundings are at 250 K. By Gouy-Stodola, how much work capacity is destroyed, in joules?

4.[1p] Four distinguishable particles are spread between the two halves of a box, giving 16 microstates in all. How many of them put exactly three particles on the left?

5.[3p] Why must entropy be the logarithm of the multiplicity rather than some other function of it?

6.[2p] Counting microstates gives a different entropy change for the free expansion than Clausius's δQrev/T does.

7.[3p] Which statements about the Third Law are correct?

8.[2p] Put these cooling methods in order of the lowest temperature they reach, warmest first.

9.[2p] Match each process to the entropy it generates.

1.[2p]
A gas expands freely into an evacuated vessel inside rigid insulated walls. Which set of values is correct?

2.[3p]
Two moles of an ideal gas expand freely from $5$ litres to $15$ litres inside rigid insulated walls. What entropy is generated, in J K⁻¹?

3.[3p]
$500$ J of heat leaks from a reservoir at $400$ K into one at $250$ K, and the surroundings are at $250$ K. By Gouy-Stodola, how much work capacity is destroyed, in joules?

4.[1p]
Four distinguishable particles are spread between the two halves of a box, giving $16$ microstates in all. How many of them put exactly three particles on the left?

5.[3p]
Why must entropy be the logarithm of the multiplicity rather than some other function of it?

6.[2p]
Counting microstates gives a different entropy change for the free expansion than Clausius's $δ Q_{r e v} / T$ does.

7.[3p]
Which statements about the Third Law are correct?

8.[2p]
Put these cooling methods in order of the lowest temperature they reach, warmest first.

9.[2p]
Match each process to the entropy it generates.