An ideal gas (γ = 1.5) undergoes a change in state such that the magnitude of heat absorbed by the g — Thermodynamics and Thermochemistry Chemistry Question

💡 Solution & Explanation

In a polytropic process PV^n = constant, work done BY the gas is W = nR*dT/(n-1), and heat absorbed is Q = n*C*dT. For Q = W to hold, we require C = R / (n-1). Also, C = $C_v$ + R/(1-n). Given γ = 1.5, $C_v$ = R/(γ - 1) = 2R. Thus, C = 2R - R/(n-1). Equating these two expressions: R/(n-1) = 2R - R/(n-1) => 2*R/(n-1) = 2R => n - 1 = 1 => n = 2. Substituting n=2 back into C gives C = R/(2-1) = R.