All Problems

First law of thermodynamics, heat capacity

Problem 2.48

An ideal gas whose adiabatic exponent equals \(\gamma\) is expanded according to the law \(p=\alpha V,\) where \(\alpha\) is a constant. The initial volume of the gas is equal to \(V_{0}\). As a result of expansion the volume increases \(\eta\) 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.

Reveal Answer
 (a) ΔU=αV02(η2−1)/(γ−1) (b) A=1/2αV02(η2−1) (c) C=1/2R(γ+1)/(γ−1)\text { (a) } \Delta U=\alpha V_{0}^{2}\left(\eta^{2}-1\right) /(\gamma-1) \text { (b) } A=1 / 2 \alpha V_{0}^{2}\left(\eta^{2}-1\right) \text { (c) } C=1 / 2 R(\gamma+1) /(\gamma-1)
Prev
Next