For a sample of perfect gas when its pressure is changed isothermally from to , the entropy change is given by [2016]

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Q.
For a sample of perfect gas when its pressure is changed isothermally from $p_{i}$ to $p_{f}$ , the entropy change is given by [2016]

1 $Δ S = n R \ln (\frac{p_{f}}{p_{i}})$

2 $Δ S = n R \ln (\frac{p_{i}}{p_{f}})$

3 $Δ S = n R T \ln (\frac{p_{f}}{p_{i}})$

4 $Δ S = R T \ln (\frac{p_{i}}{p_{f}})$

Ans.
(2)

For an ideal gas undergoing reversible expansion, when temperature changes from $T_{i}$ to $T_{f}$ and pressure changes from $p_{i}$ to $p_{f}$ ,

$Δ S = n C_{p} \ln \frac{T_{f}}{T_{i}} + n R \ln \frac{p_{i}}{p_{f}}$

For an isothermal process, $T_{i} = T_{f}$ so, $\ln$ $1 = 0$

$∴$ $Δ S = n R \ln \frac{p_{i}}{p_{f}}$

Solution

Q.
For a sample of perfect gas when its pressure is changed isothermally from $p_{i}$ to $p_{f}$ , the entropy change is given by [2016]

1 $Δ S = n R \ln (\frac{p_{f}}{p_{i}})$

2 $Δ S = n R \ln (\frac{p_{i}}{p_{f}})$

3 $Δ S = n R T \ln (\frac{p_{f}}{p_{i}})$

4 $Δ S = R T \ln (\frac{p_{i}}{p_{f}})$

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Solution

Q. For a sample of perfect gas when its pressure is changed isothermally from pi to pf, the entropy change is given by [2016]

1 ΔS=nRln(pfpi)

2 ΔS=nRln(pipf)

3 ΔS=nRTln(pfpi)

4 ΔS=RTln(pipf)

Ans. (2) For an ideal gas undergoing reversible expansion, when temperature changes from Ti to Tf and pressure changes from pi to pf, ΔS=nCplnTfTi+nRlnpipf For an isothermal process, Ti=Tf so, ln 1=0 ∴ ΔS=nRlnpipf

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Q.
For a sample of perfect gas when its pressure is changed isothermally from $p_{i}$ to $p_{f}$ , the entropy change is given by [2016]

1 $Δ S = n R \ln (\frac{p_{f}}{p_{i}})$

2 $Δ S = n R \ln (\frac{p_{i}}{p_{f}})$

3 $Δ S = n R T \ln (\frac{p_{f}}{p_{i}})$

4 $Δ S = R T \ln (\frac{p_{i}}{p_{f}})$