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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 :

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

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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.

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5. An ideal monoatomic gas is confined in a cylinder by a spring loaded piston of cros section $8.0 \times 10^{-3} \, m^2$. Initially the gas is at 300K and occupies a volume of $2.4 \times 10^{-3} \, m^3$ and the spring is in its relaxed state as shown in figure. The gas is heated by a small heater until the piston moves out slowly by $0.1\, m$. The force constant of the spring is $8000\, N/m$ and the atmospheric pressure is $1.0 \times 10^5 \, N/m^2$. The cylinder and the piston are thermally insulated. The piston and the spring are massless and there is no friction between the piston and the cylinder. The final temperature of the gas will be :
(Neglect the heat loss through the lead wires of the heater. The heat capacity of the heater coil is also negligible)

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