For a certain gas the ratio of specific heats is given to be `gamma = 1.5`, for this gas

Options

A. `C_(v) = (3R)/(2)`
B. `C_(p) = 3R`
C. `C_(p) = (5R)/(2)`
D. `C_(p) = (5R)/(2)`

Answer

To solve the problem, we need to find the specific heat at constant pressure (Cp) for the given gas, using the provided ratio of specific heats (gamma = Cp/Cv = 1.5) and the relationship between Cp, Cv, and the gas constant (R).

### Step-by-Step Solution:

1. **Identify the given values**:
- The ratio of specific heats, \( \gamma = 1.5 \).

2. **Write the relationship between Cp and Cv**:
- We know that \( \gamma = \frac{C_p}{C_v} \).
- Therefore, we can express this as:
\[ C_p = \gamma \cdot C_v \]

3. **Use the relationship between Cp, Cv, and R**:
- We also know that:
\[ C_p - C_v = R \]

4. **Substitute the expression for Cp into the equation**:
- Substitute \( C_p = 1.5 \cdot C_v \) into the equation \( C_p - C_v = R \):
\[ 1.5 \cdot C_v - C_v = R \]
- Simplifying this gives:
\[ 0.5 \cdot C_v = R \]

5. **Solve for Cv**:
- Rearranging the equation gives:
\[ C_v = \frac{R}{0.5} = 2R \]

6. **Substitute Cv back to find Cp**:
- Now substitute \( C_v = 2R \) back into the equation for Cp:
\[ C_p = 1.5 \cdot C_v = 1.5 \cdot (2R) = 3R \]

7. **Final Result**:
- Therefore, the specific heat at constant pressure \( C_p \) for the gas is:
\[ C_p = 3R \]