Question

One mole of an ideal gas $(γ = 1.4)$ is adiabatically compressed so that its temperature rises from $27^°C$ to $35^°C$. The change in the internal energy of the gas is (given $R = 8.3\, J^{-1}\,mole^{-1}\, K^{-1}$)

• A. $- 166\, J$
• B. $166\, J$
• C. $- 168\, J$
• D. $168\, J$

Answer 1

Answer: (B)

$ΔU = C_V \,ΔT.$
Now
$C_P-C_V$ or $\frac{C_{P}}{C_{V}}-1=\frac{R}{C_{V}}$
or $C_{V}=\frac{R}{\gamma-1^{'}} \left(\because \gamma=\frac{C_{P}}{C_{V}}.\right)$
Hence $\Delta u=\frac{R\Delta T}{\left(\gamma-1\right)}=\frac{8.3\times8}{\left(1.4-1\right)}=166\,J$