For two mole of an ideal gas, the correct relation is :

Options

A. `C_(v)-C_(p)=R`
B. `C_(p)-C_(v) = 2R`
C. `C_(p)-C_(v) = R`
D. `C_(v)-C_(p) = 2R`

Explanation

To solve the problem regarding the relationship between the heat capacities \( C_p \) and \( C_v \) for 2 moles of an ideal gas, we can follow these steps:

### Step 1: Understand the Definitions
- \( C_p \) is the heat capacity at constant pressure.
- \( C_v \) is the heat capacity at constant volume.
- The difference between these two heat capacities for an ideal gas is given by the equation:
\[ C_p - C_v = nR \]
where \( n \) is the number of moles of the gas and \( R \) is the universal gas constant.

### Step 2: Identify the Given Information
- We are given that there are 2 moles of an ideal gas. Thus, \( n = 2 \).

### Step 3: Substitute the Values into the Equation
- Using the equation \( C_p - C_v = nR \), we substitute \( n = 2 \):
\[ C_p - C_v = 2R \]

### Step 4: State the Final Relation
- Therefore, the correct relation for 2 moles of an ideal gas is:
\[ C_p - C_v = 2R \]

### Conclusion
- The answer to the question is \( C_p - C_v = 2R \).

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