Question

An insulator container contains 4 moles of an ideal diatomic gas at temperature $T$. Heat $Q$ is supplied to this gas, due to which 2 moles of the gas are dissociated into atoms but temperature of the gas remains constant. Then

• A. Q = 2 R T
• B. Q = R T
• C. Q = 3 R T
• D. Q = 4 R T

Answer 1

Answer: (B)

$Q=\Delta U=U_f-U_i=$
[internal energy of 4 moles of a monoatomic gas $+$ internal energy of 2 moles of a diatomic gas] - [internal energy of 4 moles of a diatomic gas $]$
$=\left(4\times \frac{3}{2}RT+2\times \frac{5}{2}RT\right)-\left(4\times \frac{5}{2}RT\right)=RT$