For `2` mole of an ideal gas , the relation between `C_(p) & C_(v)` (non-molar) are:

Options

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

Answer

To find 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 of \( C_p \) and \( C_v \)
- \( C_p \) is the heat capacity at constant pressure, which is defined as:
\[ C_p = \left( \frac{\partial H}{\partial T} \right)_P \]
- \( C_v \) is the heat capacity at constant volume, which is defined as:
\[ C_v = \left( \frac{\partial U}{\partial T} \right)_V \]

### Step 2: Use the relationship between \( C_p \) and \( C_v \)
For an ideal gas, there is a well-known relationship between the two heat capacities:
\[ C_p - C_v = nR \]
where \( n \) is the number of moles and \( R \) is the universal gas constant.

### Step 3: Substitute the number of moles
In this case, we have 2 moles of gas, so we substitute \( n = 2 \) into the equation:
\[ C_p - C_v = 2R \]

### Step 4: Rearranging the equation
From the equation above, we can express the relationship:
\[ C_p = C_v + 2R \]

### Conclusion
Thus, the relationship between \( C_p \) and \( C_v \) for 2 moles of an ideal gas is:
\[ C_p - C_v = 2R \]