One mole of a gas is enclosed in a cylinde in a cyclinder and occupies a volume of `1.5 L` at a pressure 1.5 atm. It is subjected to strong heating due to which temperature of the gas increase according to the relation `T = alpha V^(2)`, where `alpha` is a positive constant and `V` is volume of the gas.
a. Find the work done by air in increasing the volume of gas to `9 L`.
b. Draw the `P - V` diagram of the process.
c. Determine the heat supplied to the gas (assuming `gamma = 1.5)`.

Explanation

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

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

1. **Understanding the Work Done**: The work done by the gas during expansion can be calculated using the formula:
\[ W = \int_{V_1}^{V_2} P \, dV \]
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