Question

Calculate $\Delta S$ for $3$ mole of a diatomic ideal gas which is heated and compressed from $298K$ and $1$ bar to $596K$ and $4$ bar: [Given :$C_{v,m}\left(gas\right)=\frac{5}{2}R;\ln \left(2\right)=0.70;R=2cal{K}^{-1}{mol}^{-1}$]

• A. $-14.7{cal.K}^{-1}$
• B. $+14.7{cal.K}^{-1}$
• C. $-4.9{cal.K}^{-1}$
• D. $+6.3{cal.K}^{-1}$

Answer 1

Answer: (D)

$+6.3{cal.K}^{-1}$

As we know, for reversible system :

$C_v=\frac{5}{2}R\Rightarrow C_p=\frac{7}{2}R$

$\Delta S=n{C}_{p}Rln\frac{T_2}{T_1}-nRln\frac{P_2}{P_1}=3\times \frac{7}{2}\times 2ln\frac{596}{298}-3\times 2\times ln\frac{4}{1}=6.23cal.K^{-1}$