Question

An insulated system contains $4$ moles of an ideal diatomic gas at temperature $T$. When a heat $Q$ is supplied to the gas, $2$ moles of the gas is dissociated into atoms and the temperature remained constant.Then the relation between $Q$ and $T$ is $(R=$ universal gas constant. $)$

• A. Q = RT
• B. Q = 2RT
• C. Q = 3 RT
• D. Q = 4 RT

Answer 1

Answer: (A)

Given, number of moles of an ideal diatomic gas at the temperature, $T=4$
When heat $Q$ is supplied to the gas, $2$ mole of the gas is dissociated into atoms and the temperature remains constant, therefore heat supplied = change in its internal energy
i.e., $Q=\Delta u=\left(u_f-u_i\right)$
or $Q=$ (internal energy of 4 moles of a monatomic gas $+$ internal energy of $2$ moles of diatomic gas ) - (internal energy of 4 moles of a diatomic gas)
$=\left(4\times \frac{3}{2}RT+2\times \frac{5}{2}RT\right)-\left(4\times \frac{5}{2}RT\right)$
$=6RT+5RT-10RT=RT$