Question

A container made up of insulating material 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 the temperature of the gas remains constant. Find the option that correctly represents the relation between $Q$ and $T$.

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

Answer 1

The correct option is B $Q=RT$

Before disassociation, we have 4 moles of diatomic gas at temperature $T$.
After disassociation, 2 moles of diatomic gas will remain in the container at temperature $T$ and 2 moles of diatomic gas will be converted into 4 moles of monoatomic gas at temperature $T$.
The volume of the container remains same before and after the disassociation i.e no work is done in the process.
Thus, from the first law of thermodynamics, we can write
$Q=\Delta U=U_f-U_i......\left(1\right)$

Heat supplied = (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)
Using the formula $\Delta U=\frac{nfRT}{2}$ in equation $\left(1\right)$, we get
$Q=(4\times \frac{3}{2}RT+2\times \frac{5}{2}RT)-(4\times \frac{5}{2}RT)=RT$
Hence, option (b) is correct.