Question

At ${27}^{o}C$ a gas ($\gamma =5/3$) is compressed suddenly so that its pressure becomes $\frac{1}{8}$ of the original pressure. Final temperature of gas would be:

• A. $420K$
• B. $300K$
• C. ${-142}^{o}C$
• D. ${327}^{o}C$

Answer 1

Answer: (C)

${-142}^{o}C$

$P^{1-\gamma }.T^{\gamma }=$constant
$[\frac{P}{8}{]}^{1-\gamma }.T_1^{\gamma }=$constant
$\therefore [\frac{1}{8}{]}^{1-\gamma }.[\frac{T_1}{T}{]}^{\gamma }=1$
or $[\frac{T_1}{T}{]}^{\gamma }=(8{)}^{1-\gamma }=(8{)}^{1-5/3}=8^{-2/3}$
$[\frac{T_1}{T}{]}^{5/3}=(8{)}^{-2/3}$
$\therefore T_1=T\times 0.435=300\times 0.435$
$=130.58K$
${-142.4}^{o}C$