Question

One mole of an ideal gas $(\gamma =1.4)$ is adiabatically compressed so that its temperature rises from ${27}^{o}Cto{35}^{o}C$. The change in the internal energy of the gas is (given R = 80. J / mole / K)

• A. - 166 J
• B. 166 J
• C. - 168 J
• D. 168 J

Answer 1

The correct option is B

166 J

$\Delta U=C_v\Delta T.Now{C}_p-C_v=Ror\frac{C_p}{C_v}-1=\frac{R}{C_v}or{C}_v=\frac{R}{\gamma -1},where\gamma =\frac{C_p}{C_v}.Hence\Delta U=\frac{R\Delta T}{(\gamma -1)}=\frac{8.3\times 8}{(1.4-1)}=166J$