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

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$T{V}^{\gamma -1}=constant$

$\therefore \frac{T_1}{T_2}={\left(\frac{V_2}{V_1}\right)}^{\gamma -1}$ or ${\left(\frac{1}{2}\right)}^{\gamma -1}=\sqrt{\frac{1}{2}}$

$\therefore \gamma -1=\frac{1}{2}$ or $\gamma =\frac{3}{2}$ $\therefore P{V}^{\frac{3}{2}}=constant$