Question

A gas at ${27}^o$C and pressure of 30 atm. is allowed to expand to atmospheric pressure and volume 1.5 times larger. The final temperature of gas is

• A. $-{123}^0$C
• B. $+{123}^0$C
• C. ${273}^0$C
• D. ${373}^0$C

Answer 1

Answer: (A)

$-{123}^0$C

We know that $\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$
$\therefore$ $T_2=\frac{P_2{V}_2{T}_1}{P_1{V}_1}$
Here, $P_1$ = 30 atm, $P_2$ = 1 atm, $V_1$ = V (say), $V_2$ = 15 V,
$T_1={27}^o$C = 27 + 273 = ${300}^o$K and $T_2$ = ?
substituting these values, we get $T_2={150}^o$K
$\therefore$ $T_2={150}^o$K = $150-273$ = $-{123}^{o}K$