Q149 / 160 · AP EAMCET 2014 · Physics
Five moles of hydrogen initially at STP is compressed adiabatically so that its temperature becomes $673 \mathrm{~K}$. The increase in internal energy of the gas, in kilo joule is $(R=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K} ; \gamma=1.4$ for diatomic gas $)$
- A$80.5$
- B$21.55$
- Correct answerC$41.50$
- D$65.55$
Solution
Work done by an ideal gas is adiabatic expansion
$$
\begin{aligned}
& d U=n \frac{R}{\gamma-1} d T \\
& d U=n \frac{R}{\gamma-1}\left(T_2-T_1\right)
\end{aligned}
$$
Given
$$
\begin{aligned}
T_1 & =273 \mathrm{~K} \\
T_2 & =673 \mathrm{~K} \\
R & =8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K} \\
n & =5 \\
\gamma & =1.4
\end{aligned}
$$
$$
\begin{aligned}
\therefore d U & =5 \times \frac{8.3}{1.4-1}(673-273) \\
& =\frac{41.5}{0.4} \times 400 \mathrm{~J} \\
& =415 \times 100 \mathrm{~J} \\
& =41.50 \mathrm{~kJ}
\end{aligned}
$$
Hence, the correct answer is option: 'C'.