Question

Temperature of an ideal gas is $300 \, K$ . The final temperature of the gas when its volume changes from $V$ to $2V$ in the process $p=αV$ (here $\alpha $ is a positive constant) is

• A. $900 \, K$
• B. $1200 \, K$
• C. $300K$
• D. $500K$

Answer 1

Answer: (B)

The given relation is $p \propto V$
Therefore, $p \propto V$
When $V$ changes from $V$ to $2V$ , pressure $p$ is also doubled
For an ideal gas, $\frac{pV}{T}=$ constant
$\therefore \, T \propto pV$ . Hence, $T$ becomes $2\times 2=4$ times
$T=4\times 300 \, K=1200 \, K$