Thermodynamics Exercise

In a long fixed horizontal pipe, two identical pistons A and B each of mass $m$ can slide without friction. The pipe and the pistons are made of perfect heat-insulating materials. The space between the pistons is filled with $n$ mole of gaseous helium. The piston A is given an initial velocity $u$ towards the piston $B$ .

The maximum temperature change of the gas in ensuing motion of the pistons can be expressed as $\frac{mu^{\alpha}}{\beta nR},$ where $R$ is the universal gas constant.

Submit your answer as the sum of constants $\alpha +\beta$ .