An ideal gas undergoes an adiabatic process in which the temperature T is proportional to V^(-1/2), where V is the volume. Which of the following statements are correct?

The ratio of specific heats (gamma) for this gas is 1.5
V is proportional to p^(-2/3)
P is proportional to T³
P is proportional to T²

Correct answer: The ratio of specific heats (gamma) for this gas is 1.5

Solution

In an adiabatic process TV^(gamma-1) = constant. Given T proportional to V^(-1/2), we get gamma - 1 = 1/2, so gamma = 1.5. Using PV = nRT and the adiabatic relations, we can also derive how P relates to T and V.

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