Answer to Question #99928 in Molecular Physics | Thermodynamics for Jyosil Jaykrishnan

Question

Nitrogen gas is filled in an insulated container. If alpha fraction of moles dissociates without exchange of any energy then the fractional change in its temperature is:

Answer 1

1)

$$U=2.5nRT_1\to T_1=\frac{2E}{5nR}$$

2)

$$U=(1-\alpha)2.5nRT_2+(\alpha)1.5(2n)RT_2\to T_1=\frac{2E}{(5+\alpha)nR}$$

3) The fractional change in its temperature is:

$$\frac{\frac{2E}{(5+\alpha)nR}-\frac{2E}{5nR}}{\frac{2E}{5nR}}=\frac{-\alpha}{5+\alpha}$$