An ideal gas expands such that its temperature is inversely proportional to the square root of its volume (T proportional to 1 / sqrt(V)). Find the value of 2*gamma, where gamma = Cp / Cv.

Correct answer: 3

Solution

Given T proportional to 1/sqrt(V), i.e., T * V^(1/2) = constant. For an adiabatic process TV^(gamma-1) = constant. Comparing exponents: gamma - 1 = 1/2, so gamma = 3/2. Therefore 2*gamma = 3.

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