Q105 / 125 · BITSAT 2013 · Physics
A vessel containing 1 more of $\mathrm{O}_{2}$ gas (molar mass 32) at temperature $\mathrm{T}$. The pressure of the gas is p. An identical vessel containing one mole of he gas (molar mass 4 ) at temperature $2 \mathrm{~T}$ has a pressure of
- A$\mathrm{p} / 8$
- B$\mathrm{p}$
- Correct answerC$2 \mathrm{p}$
- D$8 \mathrm{p}$
Solution
Applying gas equation, $\mathrm{pV}=\mathrm{nRT}$ We can write, $\mathrm{p}_{1} \mathrm{~V}=\mathrm{n}_{1} \mathrm{RT}_{1}$ and $\mathrm{p}_{2} \mathrm{~V}=\mathrm{n}_{2} \mathrm{RT}_{2}$
$\Rightarrow \quad \frac{\mathrm{p}_{2}}{\mathrm{p}_{1}}=\frac{\mathrm{n}_{2}}{\mathrm{n}_{1}} \times \frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}}=\frac{1}{1} \times \frac{2 \mathrm{~T}}{\mathrm{~T}}=2$
$\Rightarrow \mathrm{p}_{2}=2 \mathrm{p}$
Hence, the correct answer is option: 'C'.