Question

Which of the following is incorrect, for the reversible adiabatic expansion of an ideal gas?

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

Answer 1

The correct option is D $P^{\gamma }{V}^{\gamma -1}$ = constant

For an adiabatic expansion,
$P{V}^{\gamma }$ = constant
Since, PV = RT for 1 moles of a gas
We can put V = $\frac{RT}{P}$
So, formula becomes $P(\frac{RT}{P}{)}^{\gamma }$ = constant which gives
$T^{\gamma }{P}^{1-\gamma }$ = constant
Similarly, we get $T{V}^{\gamma -1}$ = constant
but option (d) is incorrect