The ratio of the molar heat capacities of an ideal gas is `(C_p / C_v 7/6)`. Calculate the change in internal energy of 1.0mole of the gas when its temperature is raised by `50 k (a)` keeping the pressure constant , (b) keeping the volume constant and (c ) adiabatically.

Explanation

To solve the problem, we will calculate the change in internal energy of 1 mole of an ideal gas when its temperature is raised by 50 K under three different conditions: (a) at constant pressure, (b) at constant volume, and (c) adiabatically.

### Given Data:
- Ratio of molar heat capacities: \( \frac{C_p}{C_v} = \frac{7}{6} \)
- Change in temperature, \( \Delta T = 50 \, K \)
- Number of moles, \( n = 1 \)

### Step 1: Calculate \( C_p \) and \( C_v \)
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