Question

The work of $146\text{kJ}$ is performed in order to compress one kilo-mole of a gas adiabatically and in this process the temperature of the gas increases by $7^{\circ }C$. The gas is $(R=8.3{\text{J mol}}^{-1}{K}^{-1})$ find the nature of gas.

• A. $\text{Diatomic}$
• B. $\text{Triatomic}$
• C. $\text{A mixture of monoatomic and diatomic}$
• D. $\text{Monoatomic}$

Answer 1

Answer: (A)

Step 1, Given data

Work done = 146 KJ

Change in temperature = 7 degrees Celsius

Step 2, Finding the nature of gas

Increase in temperature, $\Delta T=T_2-T_1=7^{\circ }C$ = 7 K (Since it is change in temperature so its value will be same in Kelvin and degree celsius)
work done on the system,
$W=146\text{KJ}=146\times 1000\text{J}$
Number of moles of gas, $n=1000$
work done in adiabatic process,
$W=\frac{nR(T_2-T_1)}{\gamma -1}$
put the values,
$146000=\frac{1000\times 8.3\times 7}{\gamma -1}$
$\gamma -1=0.39$
$\gamma \approx 1.4$
The gas is diatomic in nature.