Question

An ideal gas at a pressure of $1$ atmosphere and temperature of ${27}^{o}C$ is compressed adiabatically until its pressure becomes $8$ times the initial pressure, then the final temperature is
($\gamma =3/2$)

• A. ${627}^{0}C$
• B. ${527}^{0}C$
• C. ${427}^{0}C$
• D. ${327}^{0}C$

Answer 1

The correct option is D ${327}^{0}C$

In an adiabatic process, pressure and temperature are related as
$P{T}^{\frac{\gamma }{\gamma -1}}=$constant
${\left(\frac{P_1}{P_2}\right)}^{1-\gamma }={\left(\frac{T_2}{T_1}\right)}^{\gamma }$
${\left(\frac{1}{8}\right)}^{1-1.5}={\left(\frac{T_2}{300}\right)}^{1.5}$
$T_2=300\times 8^{0.5/1.5}=300\left(2\right)=600K={327}^{o}C$
Option D.