# For a sample of perfect gas when its pressure is changed isothermally from pi to pf, the entropy change is given by

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

(a) $\Delta S=nR \ln({p_f\over p_i})$

(b) $\Delta S=nR \ln({p_i\over p_f})$

(c) $\Delta S=nRT \ln({p_f\over p_i})$

(d) $\Delta S=RT \ln({p_i\over p_f})$

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Ans: (b) $ΔS=nR\ln({p_i\over p_f})$

Sol: For an ideal gas undergoing reversible expansion, when temperature changes from $T_i$ to $T_f$ and pressure changes from $p_i$ to $p_f$,

$ΔS=nC_p\ln({T_f\over T_i}) + nR\ln({p_i\over p_f})$

For an isothermal process, $T_i = T_f$ so, $\ln 1 = 0$

∴ $ΔS=nR\ln({p_i\over p_f})$