Question

A perfect gas is found to obey the relation $P V^{3 / 2}=$ constant during an adiabatic process. If such a gas initially at a temperature $T$, is compressed to half of its initial volume, then its final temperature will be :

• A. $2T$
• B. $4T$
• C. $(2)^{1/2}T$
• D. $2(2)^{1/2}T$

Answer 1

Answer: (C)

$(2)^{1/2}T$

Answer 2

Gas obeys the equation
$P V^{3 / 2}=\text { constant }$
Comparing with $P V^{\gamma}=$ constant
$\gamma=\frac{3}{2}$
For arliabatic process
$T_{1} V_{1}^{\gamma-1} =T_{2} V_{2}^{\gamma-1}$
$T(V)^{3 / 2-1} =T_{2}\left(\frac{V}{2}\right)^{3 / 2-1}$
$T_{2} =T(2)^{3 / 2-1}$
$=(2)^{1 / 2} T$