Question

For an adiabatic change in a gas, if P, V, T denotes pressure, volume and absolute temperature of gas at any time and $\gamma$ is the ratio of specific heats of gas, which of the following equation is true?

• A. $T^{\gamma }{P}^{1-\gamma }=const.$
• B. $T^{1-\gamma }{P}^{\gamma }=const.$
• C. $T^{\gamma -1}{V}^{\gamma }=const.$
• D. $T^{\gamma }{V}^{\gamma }=const.$

Answer 1

The correct option is A $T^{\gamma }{P}^{1-\gamma }=const.$

We know that $P{V}^{\gamma }=C$.
or
$P(\frac{nRT}{P}{)}^{\gamma }=C$
or
$P^{1-\gamma }{T}^{\gamma }=C$ (as n and R are constants)