Question

The work of $146kJ$ is performed in order to compress $1$ kilo mole of a gas adiabatically and in the process the temperature of the gas increases by $7^{\circ }C$. The gas is:

($R=8.3Jmo{l}^{-1}{K}^{-1}$)

• A. Diatomic
• B. A mixture of monoatomic and diatomic
• C. Monoatomic
• D. Triatomic

Answer 1

Answer: (A)

Diatomic

For adiabatic compression, $\Delta Q=0$

Using first law of thermodynamics,

$\Delta U=-W$

$n{C}_v\Delta T=-W$

$n\frac{f}{2}R\Delta T=-W$

$f=\frac{-2W}{nR\Delta T}$

$=\frac{-2\times -146}{1\times 8.3\times 7}$

$f\approx 5.02$

Degrees of freedom is $2$ for a diatomic gas. Hence, the gas is diatomic.