For a gas the differce between the two specific heat is `4150 J//kg K`. What is the specific heat at constant volume of gas if the ratio of sepcific heat is 1.4

Options

A. `8475 J//kg-K`
B. `5186 J//kg-K`
C. `1660 J//kg-K`
D. `10375 J//kg-K`

Explanation

To solve the problem, we need to find the specific heat at constant volume (Cv) given the difference between the specific heats (Cp - Cv) and the ratio of the specific heats (Cp/Cv).

### Step-by-Step Solution:

1. **Understand the Given Information:**
- The difference between specific heats: \( Cp - Cv = 4150 \, \text{J/kg K} \)
- The ratio of specific heats: \( \frac{Cp}{Cv} = 1.4 \)

2. **Express Cp in terms of Cv:**
- From the ratio \( \frac{Cp}{Cv} = 1.4 \), we can express Cp as:
\[ Cp = 1.4 \times Cv \]

3. **Substitute Cp in the Difference Equation:**
- Now substitute the expression for Cp into the difference equation:
\[ (1.4 \times Cv) - Cv = 4150 \]

4. **Simplify the Equation:**
- Combine like terms:
\[ 1.4Cv - Cv = 4150 \]
\[ 0.4Cv = 4150 \]

5. **Solve for Cv:**
- Now, solve for Cv by dividing both sides by 0.4:
\[ Cv = \frac{4150}{0.4} \]
\[ Cv = 10375 \, \text{J/kg K} \]

6. **Conclusion:**
- The specific heat at constant volume \( Cv \) is \( 10375 \, \text{J/kg K} \).

### Final Answer:
The specific heat at constant volume of the gas is \( 10375 \, \text{J/kg K} \).

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