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Question 9

In an Isothermal change, the change in pressure and volume of a gas can be represented for three different temperature; $$T_3 > T_2 > T_1$$ as:

For an isothermal process involving an ideal gas, we have $$PV = nRT = \text{constant}$$.

This gives the relation $$P = \frac{nRT}{V}$$, which is a rectangular hyperbola in the P-V plane.

Key properties of isothermal curves (isotherms) on a P-V diagram:

1. Each isotherm is a rectangular hyperbola.

2. For a higher temperature, the hyperbola is farther from the origin.

3. At any given volume, a higher temperature gives a higher pressure (since $$P = \frac{nRT}{V}$$).

Since $$T_3 > T_2 > T_1$$, the isotherm for $$T_3$$ should be the outermost curve (farthest from origin), $$T_2$$ in the middle, and $$T_1$$ closest to the origin.

The correct graph shows rectangular hyperbolas that do not intersect, with $$T_3$$ being the highest curve.

The answer is Option A.

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