Question

An ideal gas of adiabatic exponent $\gamma$ is expanded so that the amount of heat transferred to the gas is equal to the decrease of its internal energy. Then the equation of the process in terms of the variables $T$ and $V$ is

• A. $T{V}^{\frac{\gamma -1}{2}}=C$
• B. $T{V}^{\frac{\gamma -2}{2}}=C$
• C. $T{V}^{\frac{\gamma -1}{4}}=C$
• D. $T{V}^{\frac{\gamma -2}{4}}=C$

Answer 1

The correct option is A $T{V}^{\frac{\gamma -1}{2}}=C$

We know that for an adiabatic process,work-done is give as
$P{V}^{\gamma }=C$
now from ideal gas equation we know that $PV=MRT$----- ( i.e M,R=constant)
so $P=\frac{T}{V}$
we know that $\frac{C_P}{C_V}=\gamma$
so $T{V}^{\frac{\gamma -1}{2}}=C$