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  4. Logarithms of readings of pressure and volume for an ideal gas were plotted on a graph as shown in figure-3.86. By measuring the gradient, it can be shown that the gas may be :

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Q. Logarithms of readings of pressure and volume for an ideal gas were plotted on a graph as shown in figure-3.86. By measuring the gradient, it can be shown that the gas may be :Physics Question Image

Thermodynamics

Solution:

As the graph of logarithm of $P$ and $V$ is a straight line the process must be adiabatic as the process equation will be $P V^{\gamma}=$ constant or $\log (P)=-\gamma \log (V)+K$ so the negative of slope of the curve gives the value of $\gamma=7 / 5$ which is for a diatomic gas.