In an adiabatic process, R = \(\frac{2}{3}C_V\). The pressure of the gas will be proportional to :
Answer & explanation
Correct answer: option 2
\(R = \frac{2}{3}C_V\)
We know : C_P - C_V = R
\(\gamma - 1 = \frac{R}{C_v}\)
\(R = C_V(\gamma - 1)\)
Comparing : \(\gamma = \frac{5}{3}\)
P\(1-\gamma\)T\(\gamma\) = constant = K
\(P \propto T^{\frac{\gamma}{\gamma - 1}} \text{ ... [given : } \gamma = \frac{5}{3}]\)
\(\frac{\gamma}{\gamma - 1} = \frac{5}{2}\)
\(P \propto T^{5/2}\)