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 α is a positive constant) is

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 α is a positive constant) is (A) 900 K (B) 1200 K (C) 300K (D) 500K

Tardigrade Admin · Accepted Answer

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, (pV/T)= constant ∴ T propto pV . Hence, T becomes 2× 2=4 times T=4× 300 K=1200 K

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

$900 K$

$1200 K$

$300 K$

$500 K$

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

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

900K

1200K

300K

500K