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, $T_1 = 27^°C$
$= 27 + 273 = 300 \,K$
$P_{2}=8P_{1}, T_{2}=?, \gamma=\frac{3}{2}$
As changes are adiabatic,
$\therefore P_{1}^{\gamma-1}T_{1}^{-\gamma}=P_{2}^{\gamma-1}T_{2}^{-\gamma}$
$\left(\frac{T_{2}}{T_{1}}\right)^{-\gamma}=\left(\frac{P_{1}}{P_{2}}\right)^{\gamma-1}$
$T_{2}=T_{1}\left(\frac{P_{2}}{P_{1}}\right)^{\gamma-1/\gamma}=300\left(8\right)^{\left(1.5-1\right)/1.5}=300\left(8\right)^{1/3}$
$T_{2}=600\,K=\left(600-273\right)^{°}C=327^{°}C$