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An ideal gas is taken through a process in which the pressure and the volume are changed according to the equation p = kV. Show that the molar heat capacity of the gas for the process is given by C = Cv + R/2.

An ideal gas is taken through a process in which the pressure and the volume are changed according to the equation p = kV. Show that the molar heat capacity of the gas for the process is given by C = Cv + R/2.

Grade:upto college level

2 Answers

Kevin Nash
askIITians Faculty 332 Points
8 years ago
Sol. P = KV ⇒ nRT/V = KV ⇒ RT = KV^2 ⇒ R ∆T = 2KV ∆U ⇒ R∆T/2KV = dv dQ = du + dw ⇒ mcdT = C base VdT + pdv ⇒ msdT = C base VdT + PRdF/2KV ⇒ ms = C base V + RKV/2KV ⇒ C base p + R/2
s rohin
13 Points
3 years ago
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