The difference between `C_(p)` and `C_(v)` can be derived using the empirical relation H = U + pV. Calculate the difference between `C_(p)` and `C_(v)` for 10 moles of an ideal gas.

Explanation

To find the difference between \( C_p \) and \( C_v \) for 10 moles of an ideal gas, we will use the relationship derived from the empirical relation \( H = U + pV \).

### Step-by-Step Solution:

1. **Understanding the Definitions**:
- \( C_p \) is the heat capacity at constant pressure.
- \( C_v \) is the heat capacity at constant volume.
- The relationship between the change in enthalpy (\( \Delta H \)) and the change in internal energy (\( \Delta U \)) for an ideal gas can be expressed as:
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