Gaseous State

Assertion: The graph between $ pV $ and $ \frac{1}{V} $ is a straight line.

Reason: For an adiabatic process, $ p \propto \frac{1}{V} $.

Explanation:

The graph between $ p $ and $ \frac{1}{V} $ is indeed a straight line. This follows from Boyle's law:

$ p \propto \frac{1}{V} $

(where $ n $ is the number of moles and $ T $ is the temperature)

In other words,

$ pV = \text{{constant}} $

However, for an adiabatic process, the statement $ p \propto \frac{1}{V} $ is not accurate. In an adiabatic process, $ \Delta q = 0 $, which means that $ q $ (the heat exchange) is constant, not the temperature, leading to a more complex relationship between $ p $ and $ V $.

Hence, the assertion is true, but the reason is false.

Thus, option (C) is the correct answer.