Question

$146kJ$ work is performed in order to compress 1 kilomole of gas adiabatically and in this process the temperature of the gas increases by $7^{o}C$. The gas is:
(Take $R=8.3Jmol{e}^{-1}{K}^{-1}$)

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

Answer 1

The correct option is B diatomic

Work done in an adiabatic compression process is
$W=nR\left(\frac{T_f-T_i}{\gamma -1}\right)$ ....(1)
Given:
$W=146kJ=146\times {10}^{3}J$
$n={10}^3$ since one kilo mole is ${10}^3$ moles
$T_f-T_i=7^{o}C$
Substituting the values in eqn(1) we get,
$146\times {10}^3={10}^3\times \times 8.3\times 7\times \frac{1}{\gamma -1}$
$\Rightarrow \gamma -1=0.4$
$\Rightarrow \gamma =1.4$
For an diatomic molecule: $\gamma =\frac{2+f}{f}=\frac{2+5}{5}=1.4$
Hence, the gas is diatomic.