Q. The temperature of a hypothetical gas increases to $\sqrt{2}$ times when compressed adiabatically to half the volume. Its equation can be written as
A) $PV^{3/2} =$ constant
B) $PV^{5/2} =$ constant
C) $PV^{7/3} =$ constant
D) $PV^{4/3} =$ constant
Explanation
(a) $TV^{\gamma - 1} =$ constant
$\therefore\frac{T_{1}}{T_{2}} = \left( \frac{V_{2}}{V_{1}} \right)^{\gamma - 1}\ or\ \left( \frac{1}{2} \right)^{\gamma - 1} = \sqrt{\frac{1}{2}}$
$\therefore\ \gamma - 1 = \frac{1}{2}$ or $\gamma = \frac{3}{2}\ \ \ \therefore PV^{3/2} =$ constant
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.