Question

A gas at a pressure of $5.0atm$ is heated from $0^{\circ }$ to $546^{\circ }C$ and simultaneously compressed to one-third of its original volume. Hence final pressure is

• A. $10.0atm$
• B. $30.0atm$
• C. $45.0atm$
• D. $5.0atm$

Answer 1

Answer: (C)

$P_1=5.0atm$ , $T_1=0^{\circ }C=273K,V_1=V$
$P_2$ =? $T_2=546^{\circ }C=819K,V_2=\frac{1}{3}V$
$\therefore$ From $\frac{P_1{V}_1}{P_2{V}_2}=\frac{T_1}{T_2}$
$\Rightarrow \frac{5\times V}{P_2\times \frac{1}{3}V}=\frac{273}{819}$
$\Rightarrow \frac{5\times 3}{P_2}=\frac{1}{3}$
$\Rightarrow P_2=45atm$