During an adiabatic process, the pressure of a gas is proportional to the cube of its temperature. The value…

1. $\frac{7}{5}$
2. $\frac{4}{5}$
3. $\frac{5}{3}$
4. $\frac{3}{2}$

Solution

In adiabatic process
Given, $\quad p \propto T^3$ or $p=k T^3$ $\begin{aligned} & =k\left(\frac{p V}{R}\right)^3 \\ & =\left(\frac{k}{R^3}\right) p^3 V^3 \\ \text { or } \quad p & =\left(\frac{k}{R^3}\right) p^3 V^3 \\ \Rightarrow \quad p^2 V^3 & =k \end{aligned}$
Comparing Eqs. (i) and (ii) we get $\gamma=\frac{3}{2}=\frac{C_p}{C_V}$

Asked in: AP EAMCET 2011

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