During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its…

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of $\frac{C_p}{C_v}$ for the gas is
  1. $\frac{4}{3}$
  2. 2
  3. $\frac{5}{3}$
  4. $\frac{3}{2}$

Solution

According to question,
$\begin{aligned}
& p \propto T^3 \\
& p V=n R T \\
& \text { and } p \propto T^3 \\
& P \propto(p V)^3 \\
& \Rightarrow p^2 V^3=\text { constant } \\
& p V^{3 / 2}=\text { constant } \\
& \because p V^\gamma=\text { constant } \\
& \therefore \gamma=\frac{3}{2}
\end{aligned}$ /

Asked in: NEET 2013 (All India)

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