Question

The work of 146 kJ is performed in order to compress one kilo mole of gas adiabatically and in this process the temperature of the gas increases by $7^{o}C$. The gas is $(R=8.3Jmo{l}^{-1}{K}^{-1})$

• A. monoatomic
• B. diatomic
• C. triatomic
• D. a mixture of monoatomic and diatomic

Answer 1

The correct option is B diatomic

Given : $\Delta T=-7^{o}C$ $R=8.3Jmo{l}^{-1}{K}^{-1}$ $n=1000$

Work done in compression $W_{comp}=-146KJ$

Workdone in adiabatic process $W=\frac{nR\Delta T}{\gamma -1}$

$\therefore$ $-146\times {10}^3=\frac{1000\times 8.3\times (-7)}{\gamma -1}$

OR $\gamma -1=0.39$ $⟹\gamma \approx 1.4$

Thus, the gas is diatomic in nature.