The temperature of a hypothetical gas increases to $\sqrt{2}$ times when compressed adiabatically to

Question

The temperature of a hypothetical gas increases to $\sqrt{2}$ times when compressed adiabatically to half the volume. Its equation can be written as

Professor PC Thomas Classes · Answer

Adiabatic relation $TV^{\gamma-1} = 	ext{const}$ yields $PV^{3/2} = 	ext{const}$.