Question

The temperature of a gas at pressure $P$ and volume $V$ is ${27}^{\circ }\text{C}$. Keeping its volume constant, if its temperature is raised to ${927}^{\circ }\text{C}$, then its pressure will be -

• A. $2P$
• B. $3P$
• C. $4P$
• D. $6P$

Answer 1

The correct option is C $4P$

The ideal gas equation states that,
$PV=nRT$
So, we can conclude from the data given in the question that,
$P\propto T$ $($As $V$ is constant$)$
Hence, $\frac{P_1}{P_2}=\frac{T_1}{T_2}........\left(1\right)$
Given, $T_1=300\text{K},T_2=1200\text{K},P_1=P$
$\therefore$ From $\left(1\right)$, we can write that
$P_2=\frac{P_1{T}_2}{T_1}$
$\Rightarrow P_2=\frac{P\times 1200}{300}$
$\Rightarrow P_2=4P$
Thus, option (c) is the correct answer.