Question

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

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

Answer 1

The correct option is C $45.0$atm

$\begin{array}{c}\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}\\ P_1=5,T_1=273+0=273\\ T_2=273+546=819K\\ V_2=\frac{V_1}{3}\\ \frac{5\times V_1}{273}=\frac{P_2\times V_1/3}{819}\\ P_2=\frac{5\times 3\times 819}{273}=45atm\end{array}$