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Thermal Physics > Topic 4 > Flashcards

Topic 4 Flashcards

1
Q

What is Clausiusโ€™ theorem for a reversible closed cycle?

A

For the Carnot Cycle:
โˆฎd๐‘„/๐‘‡=0

  • Isothermal path: dQ=dW=-nRln(V2/V1) since dU= 0
  • Adiabatic path: dQ=0
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2
Q

What is Clausiusโ€™ inequality for any cycle?

A
  • General Cycle
  • dQ for a series of Carnot engine, does work and does not output any heat

Kelvin statement leads to clausis inequality

โˆฎd๐‘„/๐‘‡โ‰ค0

Equality corresponds to a reversible process

Heat in - dQ= nRTln(V2/V1) and negative for heat out

Carnot cycle is reversible
Net work out = the modulus of the work

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3
Q

What is entropy?

A

Defined by S

d๐‘†=(ฤ‘๐‘„_rev)/๐‘‡

It is a function of state
Units: JK^-1

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4
Q

What is the entropy change along an adiabatic path?

A

For an adiabatic change of state ฤ‘Q = 0
There is no change in entropy along a reversible adiabatic path
(not true of an irreversible adiabatic change)

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5
Q

What is the entropy change along an reversible isothermal path?

A

For an isothermal change of state,

ฮ”๐‘†=๐‘„/๐‘‡

where Q is the heat transferred into the system along the path (if the system discards heat, Q < 0)

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6
Q

What is greater reversible or irreversible?

A

d๐‘†=(ฤ‘๐‘„_rev)๐‘‡โ‰ฅฤ‘๐‘„/๐‘‡

reversible > irreversible

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7
Q

What is the equation for entropy for a thermally isolated system?

A

d๐‘†โ‰ฅ0

since ฤ‘Q = 0

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8
Q

What is the entropy statement of the second law?

A

A process cannot occur if it would result in a decrease in the total entropy of the Universe

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9
Q

How do you calculate entropy in irreversible processes?

A

Since entropy is a function of state
we can find a reversible path between the initial and final states

we can calculate the change in entropy of the system using that path

(change in entropy of the Universe will not be the same for the reversible and irreversible processes)

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10
Q

What is the entropy change around a closed reversible cycle?

A

d๐‘†=0

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11
Q

What is the entropy changes for a reversible cycle (regarding heat engines)?

A

ฮ”S (system) = ฮ”S(surroundings) = 0

ฮ”S(Universe) = ฮ”S (system) + ฮ”S(surroundings) = 0

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12
Q

What is the entropy changes for a reversible change of state (A โ†’ B)?

A

ฮ”S (system) = โˆ’ฮ”S(surroundings) [can be positive, negative or zero]
ฮ”S(Universe) = ฮ”S (system) + ฮ”S(surroundings) = 0

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13
Q

What is the entropy changes for an irreversible cycle?

A

ฮ”S (system) = 0; ฮ”S(surroundings) > 0

ฮ”S(Universe) = ฮ”S (system) + ฮ”S(surroundings) > 0

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14
Q

What is the entropy changes for an irreversible change of state (A โ†’ B)?

A

ฮ”S (system) โ‰  โˆ’ฮ”S(surroundings)

ฮ”S(Universe) = ฮ”S (system) + ฮ”S(surroundings) > 0

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15
Q

What is the central equation of thermodynamics?

A

The first law in a path independent form in terms of entropy changes:

dU=TdS -pdV
Leads to:
๐‘‡=(๐œ•๐‘ˆ/๐œ•๐‘†)_๐‘‰ ๐‘=โˆ’(๐œ•๐‘ˆ/๐œ•๐‘‰)_๐‘†

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16
Q

What is the equations used in irreversible joule expansion (irreversible adiabatic change of state)?

A
  • Thermally isolated container (ideal gas pi and Vi)
  • Rest is a vacuum
  • Remove partition allowing it flow into the evacuated region

Entropy is a state function so we just need to find the reversible path between the initial and final state

dU=0 as only U depends on T for a gas at constant T so we need to find the entropy change using a reversible thermal path

dU=dW=dQ=0
ฮ”๐‘†_surroundings=0
ฮ”๐‘†_Universe=ฮ”๐‘†_system=๐‘›๐‘… lnโก(๐‘‰_๐‘“ /๐‘‰_๐‘– ) > 0

17
Q

What is the equations used in reversible expansion?

A 
ฮ”๐‘†_system=๐‘›๐‘… lnโก(๐‘‰_๐‘“ /๐‘‰_๐‘– )
ฮ”๐‘†_surroundings=โˆ’๐‘›๐‘… lnโก(๐‘‰_๐‘“ /๐‘‰_๐‘– )
ฮ”๐‘†_Universe=0
๐‘‘๐‘ˆ=0
๐‘‘๐‘Š=โˆ’๐‘๐‘‘๐‘‰
๐‘‘๐‘„=โˆ’๐‘‘๐‘Š=๐‘๐‘‘๐‘‰
18
Q

What is the change in entropy for (MIXING) irreversible, adiabatic change of state?

A
  • Thermally isolated container (ideal gas pi and Vi)
  • Other part is filled with different ideal gas
  • Open partition of the two and they mix
  • Liked two combined joule expansion

ฮ”๐‘†=โˆ’๐‘›๐‘…(๐‘ฅ lnโก๐‘ฅ+(1โˆ’๐‘ฅ) lnโก(1โˆ’๐‘ฅ) )

19
Q

What is the maximum of the entropy of an isolated system?

A

Attains this maximum at equilibrium, this means that any change in entropy away from equilibrium would serve decrease entropy which is not allowed by the second law

20
Q

What is Boltzmannโ€™s relation?

A

๐‘†=๐‘˜_๐ต lnโก๐‘Š

  • LHS Gives the macroscopic view
  • RHS Gives the microscopic view
21
Q

What is the total number of combined ways?

A

W_t=W_1W_2

22
Q

Why does water not like to mix with non-polar molecules?

A

Due to entropy decrease

23
Q

What happens in the local changes in entropy?

A

The second law does not forbid local decrease of a system THAT IS NOT ISOLATED (changes of states e.g crystallisation, biological growth)

the entropy of the universe must not decrease (local decrease compensated by increased entropy of the system)

Thermal Physics (6 decks)

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