Question

During an adiabatic process, the pressure of a gas is found to be proportional to $4$ power of its absolute temperature. The $\gamma$ for the gas is

• A. $\frac{4}{3}$
• B. $\frac{3}{4}$
• C. $\frac{3}{2}$
• D. $\frac{5}{3}$

Answer 1

Answer: (A)

According to the given question
$P\propto T^4$
or $P{T}^{-4}$ = constant $\dots \left(i\right)$
For an adiabatic process
$P{T}^{\gamma /1-\gamma }$ =constant $\dots \left(ii\right)$
Comparing $\left(i\right)$ and $\left(ii\right)$, we get
$\therefore \frac{\gamma }{1-\gamma }=-4$
or $\gamma =-4+4\gamma$
$3\gamma =4$
$\gamma =\frac{4}{3}$