An ideal gas is expanding such that p T 2 = constant. The coefficient of volume expansion of the gas is

Question

An ideal gas is expanding such that p T 2 = constant. The coefficient of volume expansion of the gas is, 1 T, 2 T, 3 T, 4 T

MARKS App · Accepted Answer

Given, p T 2 = constant ∴ n R T V T 2 = constant or T 3 V - 1 = constant Differentiating the equation, we get 3 T 2 V . d T - T 3 V 2 . d V = 0 or 3 . d T = T V . d V From the equation, d V = V γ d T γ = coefficient of volume expansion of gas = d V V . d T ∴ γ = d V V . d T = 3 T

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