Question

The work of 146 kJ is performed in order to compress one kilomole of a 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. Diatomic
• B. Triatomic
• C. A mixture of monoatomic and diatomic
• D. None of the above

Answer 1

The correct option is A Diatomic

For Adiabatic process,

$dQ=0$

$\Rightarrow$ $dU=△W$

or $n{C}_{v}dT=+146\times {10}^{3}J$

$\Rightarrow$ $\frac{nfR}{2}\times 7=146\times {10}^{3}J$

where, f is degree of freedom.

$\Rightarrow$ $\frac{{10}^3\times f\times 8.3\times 7}{2}=146\times {10}^{3}J$

$f=5.02\simeq 5$

Therefore, gas is diatomic.