Question

The work of 146 KJ is performed in order to compress on kilo mole of a gas adiabatically and in this process the temperature of the gas increases by $7^0$C. The gas is $(R=8.3Jmo{l}^{-1}{K}^{-1})$

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

Answer 1

The correct option is A diatomic

Given : Increase in temperature, $\Delta T=T_2-T_1=7^{o}C$

Work done on the system, $W=146kJ=146\times 1000J$

Number of moles of gas, $n=1000$

Work done in adiabatic process, $W=\frac{nR(T_2-T_1)}{\gamma -1}$

$\Rightarrow 146000=\frac{1000\times 8.3\times 7}{\gamma -1}$

$\Rightarrow$ $\gamma -1=0.39$

$\Rightarrow \gamma \approx 1.4$

$\Rightarrow$ The gas is diatomic in nature.