Calculate the difference between `C_p and C_(V)` for 10 mole of an ideal gas.

Options

A. 83.14 J
B. 8.314 J
C. 831.4 J
D. 0.8414 J

Explanation

To calculate the difference between \( C_p \) and \( C_v \) for 10 moles of an ideal gas, we can use the formula:

\[ C_p - C_v = nR \]

where:
- \( C_p \) is the specific heat at constant pressure,
- \( C_v \) is the specific heat at constant volume,
- \( n \) is the number of moles, and
- \( R \) is the universal gas constant.

### Step-by-step Solution:

1. **Identify the values**:
- Given \( n = 10 \) moles (the number of moles of the gas).
- The value of the gas constant \( R = 8.314 \, \text{J/mol·K} \).

2. **Substitute the values into the formula**:
\[ C_p - C_v = nR \]
Substituting \( n = 10 \) and \( R = 8.314 \):
\[ C_p - C_v = 10 \times 8.314 \]

3. **Calculate the product**:
\[ C_p - C_v = 83.14 \, \text{J} \]

4. **Conclusion**:
The difference between \( C_p \) and \( C_v \) for 10 moles of an ideal gas is \( 83.14 \, \text{J} \).

### Final Answer:
\[ C_p - C_v = 83.14 \, \text{J} \]

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