Question

An ideal gas at a pressure of 1 atmosphere and temperature of $27^{°}C$ is compressed adiabatically until its pressure becomes 8 times the initial pressure. Then the final temperature is $\left(\gamma =\frac{3}{2}\right)$

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

Answer 1

Answer: (D)

Here, $P_1=1$ atm, $T_1=27^{°}C$
$=27+273=300K$
$P_2=8P_1,T_2=?,\gamma =\frac{3}{2}$
As changes are adiabatic,
$\therefore P_1^{\gamma -1}{T}_1^{-\gamma }=P_2^{\gamma -1}{T}_2^{-\gamma }$
${\left(\frac{T_2}{T_1}\right)}^{-\gamma }={\left(\frac{P_1}{P_2}\right)}^{\gamma -1}$
$T_2=T_1{\left(\frac{P_2}{P_1}\right)}^{\gamma -1/\gamma }=300{\left(8\right)}^{\left(1.5-1\right)/1.5}=300{\left(8\right)}^{1/3}$
$T_2=600K={\left(600-273\right)}^{°}C=327^{°}C$