UPSC NDA II 2018 General Ability Solved Paper

Concept:The ideal gas law $PV = \mu RT$ relates pressure, volume, temperature, and number of moles for ideal gases.Explanation:Both Ar and CO₂ are ideal gases, and the chamber volume $V$ and temperature $T$ remain the same.For Ar: number of molecules $n$ corresponds to moles $\mu = \frac{n}{N_A}$, but using the ideal gas law in terms of molecules gives $PV = nkT$ where $k$ is Boltzmann's constant. Alternatively, using moles: $PV = \mu RT$.Let $PV = nkT$ (if $n$ is number of molecules) or $PV = \frac{n}{N_A}RT$. Both forms yield the same ratio.Step 1: For Ar gas, $PV = nkT$ (or equivalently $PV = \mu RT$ with $\mu = \frac{n}{N_A}$).Step 2: For CO₂ gas, number of molecules is $\frac{n}{2}$, so $P'V = \frac{n}{2}kT$.Step 3: Divide the CO₂ equation by the Ar equation: $\frac{P'V}{PV} = \frac{\frac{n}{2}kT}{nkT}$ → $\frac{P'}{P} = \frac{1}{2}$.Step 4: Hence $P' = \frac{P}{2}$.Answer:$P' = \frac{P}{2}$, which corresponds to option C.