Lesson test: Entropy

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Entropy

1.[2p]
What does $\oint δ Q_{r e v} / T = 0$ for every reversible cycle establish?

That $δ Q_{r e v} / T$ is the differential of a state function

Correct

That heat is conserved round a reversible cycle

The answer is: That $δ Q_{r e v} / T$ is the differential of a state function

That no reversible cycle can produce work

The answer is: That $δ Q_{r e v} / T$ is the differential of a state function

That temperature is constant round a reversible cycle

The answer is: That $δ Q_{r e v} / T$ is the differential of a state function

2.[3p]
A gas expands irreversibly into a vacuum. How is its entropy change found?

Integrate $δ Q_{r e v} / T$ along any invented reversible path between the same two states

Correct

Integrate $δ Q / T$ along the actual process, which gives zero

The answer is: Integrate $δ Q_{r e v} / T$ along any invented reversible path between the same two states

It cannot be found, because the process is irreversible

The answer is: Integrate $δ Q_{r e v} / T$ along any invented reversible path between the same two states

Divide the work done by the initial temperature

The answer is: Integrate $δ Q_{r e v} / T$ along any invented reversible path between the same two states

3.[2p]
Two kilograms of ice melt at $0$ °C. The latent heat of fusion is $334$ kJ/kg. What is the entropy change of the ice, in J/K?

CorrectNot quite: 2445.5

4.[2p]
One mole of an ideal gas expands isothermally and reversibly to twice its volume. What is its entropy change, in J/K? Take $R = 8.314$ J/(mol K).

CorrectNot quite: 5.76

5.[1p]
The entropy of a system can only ever increase.

True

The answer is: False

False

Correct

6.[2p]
In the balance $Δ S = \int δ Q / T + S_{g e n}$ , what is $S_{g e n}$ ?

Entropy manufactured inside the system by irreversibility, never negative

Correct

Entropy carried across the boundary by heat

The answer is: Entropy manufactured inside the system by irreversibility, never negative

The entropy of the surroundings

The answer is: Entropy manufactured inside the system by irreversibility, never negative

A correction term that vanishes for real processes

The answer is: Entropy manufactured inside the system by irreversibility, never negative

7.[3p]
Which of these are true of the relation $d U = T d S - p d V$ ?

Select all that apply

It holds for irreversible processes as well as reversible ones

Correct

Every quantity appearing in it is a property of the state

Correct

$T d S$ is always equal to the heat transferred

The answer is: It holds for irreversible processes as well as reversible ones, Every quantity appearing in it is a property of the state

$p d V$ is always equal to the work done

The answer is: It holds for irreversible processes as well as reversible ones, Every quantity appearing in it is a property of the state

8.[2p]
Put the steps of the argument in the order the lesson develops them.

Kelvin-Planck applied to an arbitrary cycle gives $\oint δ Q / T \leq 0$
A reversible two-reservoir cycle gives $Q_{H} / T_{H} + Q_{C} / T_{C} = 0$
A mesh of small Carnot cycles extends this to $\oint δ Q_{r e v} / T = 0$
A vanishing integral round every closed path means a state function exists

Show the answer

a, b, c, d

9.[2p]
Match each term to what it means.

Isentropic
Isentropic efficiency
Clausius inequality
Entropy transfer

the part of $Δ S$ carried by heat
adiabatic and reversible, so $Δ S = 0$
actual work over ideal work for a turbine
$\oint δ Q / T \leq 0$ for any cycle

Show the answer

Isentropic: adiabatic and reversible, so $Δ S = 0$ Isentropic efficiency: actual work over ideal work for a turbine Clausius inequality: $\oint δ Q / T \leq 0$ for any cycle Entropy transfer: the part of $Δ S$ carried by heat

1.[2p] What does ∮δQrev/T=0 for every reversible cycle establish?

2.[3p] A gas expands irreversibly into a vacuum. How is its entropy change found?

3.[2p] Two kilograms of ice melt at 0 °C. The latent heat of fusion is 334 kJ/kg. What is the entropy change of the ice, in J/K?

4.[2p] One mole of an ideal gas expands isothermally and reversibly to twice its volume. What is its entropy change, in J/K? Take R=8.314 J/(mol K).

5.[1p] The entropy of a system can only ever increase.

6.[2p] In the balance ΔS=∫δQ/T+Sgen, what is Sgen?

7.[3p] Which of these are true of the relation dU=TdS−pdV?

8.[2p] Put the steps of the argument in the order the lesson develops them.

9.[2p] Match each term to what it means.

1.[2p]
What does $\oint δ Q_{r e v} / T = 0$ for every reversible cycle establish?

2.[3p]
A gas expands irreversibly into a vacuum. How is its entropy change found?

3.[2p]
Two kilograms of ice melt at $0$ °C. The latent heat of fusion is $334$ kJ/kg. What is the entropy change of the ice, in J/K?

4.[2p]
One mole of an ideal gas expands isothermally and reversibly to twice its volume. What is its entropy change, in J/K? Take $R = 8.314$ J/(mol K).

5.[1p]
The entropy of a system can only ever increase.

6.[2p]
In the balance $Δ S = \int δ Q / T + S_{g e n}$ , what is $S_{g e n}$ ?

7.[3p]
Which of these are true of the relation $d U = T d S - p d V$ ?

8.[2p]
Put the steps of the argument in the order the lesson develops them.

9.[2p]
Match each term to what it means.