Define `C_p` and `C_V`. Why is `C_P gt C_V` ? For an ideal gas, prove that `C_P - C_V = R` .

Explanation

To solve the question, we will break it down into several steps, defining \( C_p \) and \( C_v \), explaining why \( C_p > C_v \), and proving that \( C_p - C_v = R \) for an ideal gas.

### Step 1: Define \( C_p \) and \( C_v \)

- **Definition of \( C_p \)**:
\( C_p \) is defined as the heat required to raise the temperature of one mole of an ideal gas by 1 degree Celsius (or 1 Kelvin) while keeping the pressure constant. Mathematically, this can be expressed as:
\[
Q = n C_p \Delta T
...