Question

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

• A. $450K$
• B. $300K$
• C. $-{142}^{o}C$
• D. ${327}^o$

Answer 1

The correct option is C $-{142}^{o}C$

since gas is compressed suddenly, gas is undergone an adiabatic process

In adiabatic process,

$P{V}^{\gamma }=constant$

for an ideal gas,

$\frac{PV}{T}=constant$

$\therefore P{\left(\frac{T}{P}\right)}^{\gamma }=P^{1-\gamma }{T}^{\gamma }=constant$

$\therefore {P_1}^{1-\left(5/3\right)}{T_1}^{5/3}={\left(\frac{P_1}{8}\right)}^{1-\left(5/3\right)}{T}^{5/3}$

$\frac{300}{T}=4^{3/5}$

$T=130.58K={-142.58}^{\circ }C$

Hence, option C is correct