Question

For an adiabatic compression the quantity $PV$

• A. increases
• B. decreases
• C. remains constant
• D. depends on $\gamma$

Answer 1

The correct option is A increases

The equation of state is given by:
$T{V}^{\gamma -1}=constant$
$T_1{V}_1^{\gamma -1}=T_2{V}_2^{\gamma -1}$
$\frac{T_2}{T_1}=(\frac{V_1}{V_2}{)}^{\gamma -1}$
When the gas gets compressed, the temperature thus increases.
$PV=nRT$
$P_2{V}_2-P_1{V}_1=nR(T_2-T_1)$
Since temperature increases, PV also increases.
Hence option A is correct.