10 moles of a gas are heated at constant volume from `20^@C" to "30^@C`. Calculate the change in the internal energy of the gas. The molar heat capacity of the gas at constant pressure, `C_p = 6.82 cal K^(-1) mol^(-1)` and `R = 1.987 cal K^(-1) mol^(-1)`.

Explanation

To calculate the change in the internal energy of the gas when it is heated at constant volume, we can follow these steps:

### Step 1: Identify the given data
- Number of moles of gas (n) = 10 moles
- Initial temperature (T1) = 20°C = 293 K (since 20 + 273 = 293)
- Final temperature (T2) = 30°C = 303 K (since 30 + 273 = 303)
- Molar heat capacity at constant pressure (C_p) = 6.82 cal K^(-1) mol^(-1)
- Universal gas constant (R) = 1.987 cal K^(-1) mol^(-1)
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