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Assuming, $R=8.3 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$ and $\gamma=1.4$ the values of $C_{p}$ and $C_{V}$ of a gas are
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The correct answer is:
$29.05 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}, 20.75 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$
Given, $\gamma=1.4=\frac{C_{p}}{C_{V}}$
$\Rightarrow \quad C_{p}=1.4 C_{V}$
Also, $\quad R=C_{p}-C_{V}=8.3 \quad \text{(given)}$
$\Rightarrow \quad 1.4 C_{V}-C_{V}=8.3$
or $\quad C_{V}=\frac{8.3}{0.4}=20.75 \mathrm{Jmol}^{-1} \mathrm{~K}^{-1}$
$C_{p}=1.4 C_{V}=1.4 \times 20.75$
$=29.05 \mathrm{Jmol}^{-1} \mathrm{~K}^{-1}$
$\Rightarrow \quad C_{p}=1.4 C_{V}$
Also, $\quad R=C_{p}-C_{V}=8.3 \quad \text{(given)}$
$\Rightarrow \quad 1.4 C_{V}-C_{V}=8.3$
or $\quad C_{V}=\frac{8.3}{0.4}=20.75 \mathrm{Jmol}^{-1} \mathrm{~K}^{-1}$
$C_{p}=1.4 C_{V}=1.4 \times 20.75$
$=29.05 \mathrm{Jmol}^{-1} \mathrm{~K}^{-1}$
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