Question

An ideal gas whose adiabatic exponent equals γ is expanded according to the law p = αV , where a is a constant. The initial volume of the gas is equal to V₀. As a result of expansion the volume increases η  times. Find:

(a) the increment of the internal energy of the gas;

(b) the work performed by the gas;

(c) the molar heat capacity of the gas in the process.

Answer 1

Law of the process is p = αV or pV^-1 =α

so the process is polytropic of index n = -1

AS p= αV so, p_i = αV₀ and p_f = αηV₀

(a) Increment of the internal energy is given by