If for `H_2` gas,`C_p -C_v=a` and for `O_2` gas,`C_p-C_v=b`,where `C_p` and `C_v` is heat capacity in cal/g-k,then select the correct relation

Options

A. b=8a
B. a=b
C. a=16b
D. a=4b

Answer

To solve the problem, we need to find the relationship between the values of \(C_p - C_v\) for hydrogen gas (\(H_2\)) and oxygen gas (\(O_2\)).

### Step-by-Step Solution:

1. **Understanding the Heat Capacities**:
- For any ideal gas, the relationship between the heat capacities at constant pressure (\(C_p\)) and constant volume (\(C_v\)) is given by:
\[ C_p - C_v = R/m \]
where \(R\) is the universal gas constant and \(m\) is the molar mass of the gas.

2. **Calculate for Hydrogen Gas (\(H_2\))**:
- The molar mass of \(H_2\) is:
\[ m_{H_2} = 2 \times 1 = 2 \text{ g/mol} \]
- Therefore, for \(H_2\):
\[ C_p - C_v = A = \frac{R}{2} \]

3. **Calculate for Oxygen Gas (\(O_2\))**:
- The molar mass of \(O_2\) is:
\[ m_{O_2} = 2 \times 16 = 32 \text{ g/mol} \]
- Therefore, for \(O_2\):
\[ C_p - C_v = B = \frac{R}{32} \]

4. **Finding the Ratio of A and B**:
- Now, we need to find the ratio \(A/B\):
\[ \frac{A}{B} = \frac{\frac{R}{2}}{\frac{R}{32}} = \frac{32}{2} = 16 \]

5. **Conclusion**:
- Thus, the relationship between \(A\) and \(B\) is:
\[ A = 16B \]

### Final Relation:
The correct relation is:
\[ A = 16B \]