Question

In a process, the density of a gas remains constant. If the temperature is doubled, then the change in pressure will be:

• A. $100\%$ increase
• B. $200\%$ increase
• C. $50\%$ decrease
• D. $25\%$ decrease

Answer 1

The correct option is A $100\%$ increase

We have
$\rho =\frac{PM}{RT}$
$\rho =\text{constant}$
$\Rightarrow \frac{P_{1}M}{R{T}_1}=\frac{P_{2}M}{R{T}_2}$
$\Rightarrow \frac{P_1}{T_1}=\frac{P_2}{T_2}$
$\Rightarrow \frac{P_1}{T_1}=\frac{P_2}{2T_1}$
$\Rightarrow P_2=2P_1$
Change in pressure = $\frac{P_2-P_1}{P_1}\times 100$
$=\frac{2P_1-P_1}{P_1}\times 100$
$=100\%$
Since $P\propto T$, $P$ will increase by 100%.