One mole of an ideal monatomic gas undergoes the process `p=alphaT^(1//2)`, where `alpha` is a constant.
(a) Find the work done by the gas if its temperature increases by 50K.
(b) Also, find the molar specific heat of the gas.

Explanation

To solve the given problem step by step, we will break it down into parts (a) and (b) as specified in the question.

### Part (a): Finding the Work Done by the Gas

1. **Given Relation**: We start with the relation for pressure given in the problem:
\[ P = \alpha T^{1/2} \]
...