Question

A closed cylindrical vessel contains $N$ moles of an ideal diatomic gas at a temperature $T$. On supplying heat, temperature remains same, but $n$ moles get dissociated into atoms. The heat supplied is

• A. $\frac{5}{2}(N-n)RT$
• B. $\frac{5}{2}nRT$
• C. $\frac{1}{2}nRT$
• D. $\frac{3}{2}nRT$

Answer 1

Answer: (C)

Heat supplied $=\Delta U=U_{\text{final }}-U_{\text{initial }}$
[Only diatomic gas is present]
Total intemal energy initially $=\frac{5}{2}NRT$
Total internal energy when
'$n$' moles get dissociated $=\frac{5}{2}(N-n)RT+\frac{3}{2}(2n)RT$
[diatomic and monoatomic both are present]
$\Delta U=\left\{\frac{5}{2}(N-n)RT+\frac{3}{2}(2n)RT\right\}-\frac{5}{2}NRT$
Solving this we get
$\Delta U=\frac{1}{2}nRT$
$\therefore$ Heat supplied is $\frac{1}{2}nRT$.