The difference between the principal specific heats of nitrogen is 300 J/kg K and ratio of the two specific heats is 1.4. then `C_P` is

Options

A. 1050 J/kg K
B. 750 J/kg K
C. 650 J/kg K
D. 150 J/kg K

Explanation

To solve the problem, we need to find the specific heat at constant pressure \( C_P \) given the difference between the specific heats \( C_P - C_V = 300 \, \text{J/kg K} \) and the ratio \( \frac{C_P}{C_V} = 1.4 \).

### Step-by-Step Solution:

1. **Identify the given information:**
- The difference between the specific heats:
\[ C_P - C_V = 300 \, \text{J/kg K} \]
- The ratio of the specific heats:
\[ \frac{C_P}{C_V} = 1.4 \]

2. **Express \( C_P \) in terms of \( C_V \):**
From the ratio, we can express \( C_P \) as:
\[ C_P = 1.4 C_V \]

3. **Substitute \( C_P \) into the difference equation:**
Now, substitute \( C_P \) in the difference equation:
\[ 1.4 C_V - C_V = 300 \]

4. **Simplify the equation:**
This simplifies to:
\[ 0.4 C_V = 300 \]

5. **Solve for \( C_V \):**
Dividing both sides by 0.4 gives:
\[ C_V = \frac{300}{0.4} = 750 \, \text{J/kg K} \]

6. **Find \( C_P \) using \( C_V \):**
Now, substitute \( C_V \) back into the equation for \( C_P \):
\[ C_P = 1.4 \times 750 = 1050 \, \text{J/kg K} \]

### Final Answer:
Thus, the specific heat at constant pressure \( C_P \) is:
\[ C_P = 1050 \, \text{J/kg K} \]