Four moles of a diatomic gas (g = 1.4) at a temperature of 300 K were cooled isochorically, so that the final pressure was 1/3 times the original pressure. The gas was allowed to expand isobarically till its temperature got back to its original value. Calculate the total amount of heat absorbed during the process. R = 8.31 J `mol ^(-1) K ^(-1).`

Explanation

To solve the problem step by step, we need to analyze the two processes the gas undergoes: an isochoric cooling followed by an isobaric expansion.

### Step 1: Identify the initial conditions
We have:
- Number of moles, \( n = 4 \) moles
- Initial temperature, \( T_A = 300 \) K
- Heat capacity ratio, \( \gamma = 1.4 \)

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