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Question

What is the entropy change when 1 mole oxygen gas expands isothermally and reversibly from an initial volume of 10 L to 100 L at 300 K?

A
19.14 J K1
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B
109.12 J K1
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C
29.12 J K1
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D
10 J K1
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Solution

The correct option is A 19.14 J K1
The change in entropy for the isothermal reversible process is given as :
S=2.303nR logV2V1
where V2 is the final volume and V1 is the initial volume
Putting all the values we get :
S=2.303×1×8.314× log10010=19.14 J K1


Theory:

Calculation of ΔSuniverse for an Isothermal Process:
For an isothermal process dT=0
Isothermal processes can happen reversibly and irreversibly. We have to calculate the change in entropy of the system when it is moving from state A to state B.

For a reversible isothermal process change in entropy is obtained as,
Change in entropy for system is given as,

ΔSsys=ncv,mlnT2T1+nRlnV2V1
For an isothermal process T1=T2 which makes the first term in the equation for change in entropy as zero.

Thus,
ΔSsys=nRlnV2V1

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