Mayer's kformula for the relation between two principla specific heats `C_(p) "and " C_(V)` of a gas is given by

Options

A. `C_(V)-C_(P)=R`
B. `(C_(P))/(C_(V))=R`
C. `C_(P)-C_(V)=R`
D. `(C_(V))/(C_(P))=R`

Answer

To solve the question regarding Mayer's formula for the relation between the two principal specific heats \( C_p \) and \( C_v \) of a gas, we will follow these steps:

### Step-by-Step Solution:

1. **Understanding Specific Heats**:
- The specific heat at constant pressure is denoted as \( C_p \).
- The specific heat at constant volume is denoted as \( C_v \).
- These specific heats are important in thermodynamics as they describe how much heat is required to change the temperature of a substance.

2. **Mayer's Formula**:
- Mayer's formula relates \( C_p \) and \( C_v \) with the ideal gas constant \( R \).
- The formula is given by:
\[ C_p - C_v = R \]

3. **Analyzing the Options**:
- The options provided in the question are:
1. \( C_p - C_v = R \)
2. \( \frac{C_p}{C_v} = R \)
3. \( C_p - C_v = R \)
4. \( \frac{C_v}{C_p} = R \)

4. **Identifying the Correct Relation**:
- From Mayer's formula, we see that the correct relation is:
\[ C_p - C_v = R \]
- This means that options 1 and 3 are both correct, but since they are identical, we can conclude that this is the correct expression.

5. **Final Conclusion**:
- Therefore, the correct answer is:
\[ C_p - C_v = R \]