Search any question & find its solution
Question:
Answered & Verified by Expert
The temperature of a gas contained in a closed vessel of constant volume increases by $1^{\circ} \mathrm{C}$ when the pressure of the gas is increased by $1 \%$. The initial temperature of the gas is
Options:
Solution:
1029 Upvotes
Verified Answer
The correct answer is:
$100 \mathrm{~K}$
According to Gay Lussac's law $\mathrm{p} \propto \mathrm{T}$
$$
\begin{aligned}
\therefore & \frac{\mathrm{dp}}{\mathrm{p}} \times 100=\frac{\mathrm{dT}}{\mathrm{T}} \times 100 \\
1 &=\frac{1}{\mathrm{~T}} \times 100 \\
\Rightarrow & \mathrm{T}=100 \mathrm{~K}
\end{aligned}
$$
$$
\begin{aligned}
\therefore & \frac{\mathrm{dp}}{\mathrm{p}} \times 100=\frac{\mathrm{dT}}{\mathrm{T}} \times 100 \\
1 &=\frac{1}{\mathrm{~T}} \times 100 \\
\Rightarrow & \mathrm{T}=100 \mathrm{~K}
\end{aligned}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.