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:

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