The gas of capacity 20 ml is filled with hydrogen gas. The total average kinetic – energy of translatory motion of its molecules is `1.52 xx10^4`Joules. The pressure of hydrogen in the cylinder is:

Options

A. `2 xx10^5 N//m^2`
B. `3xx10^5 N//m^2`
C. `4 xx10^5 N//m^2`
D. `5 xx10^5 N//m^2`

Explanation

To find the pressure of hydrogen gas in the cylinder, we can use the relationship between the average kinetic energy of the gas molecules and the pressure and volume of the gas. The formula we will use is:

\[ KE = \frac{3}{2} P V \]

Where:
- \( KE \) is the total average kinetic energy,
- \( P \) is the pressure,
- \( V \) is the volume.

### Step-by-step Solution:

1. **Identify the Given Values**:
- Total average kinetic energy, \( KE = 1.52 \times 10^4 \) Joules
- Volume of the gas, \( V = 20 \) ml

2. **Convert Volume to Liters**:
- Since pressure is typically measured in Pascals (N/m²), we need to convert the volume from milliliters to cubic meters.
- \( 20 \) ml = \( 20 \times 10^{-3} \) L = \( 20 \times 10^{-6} \) m³ = \( 20 \times 10^{-3} \) L = \( 20 \times 10^{-6} \) m³

3. **Substitute Values into the Kinetic Energy Formula**:
- Rearranging the formula to solve for pressure \( P \):
\[ P = \frac{2 \times KE}{3 \times V} \]
- Substitute the values:
\[ P = \frac{2 \times (1.52 \times 10^4)}{3 \times (20 \times 10^{-6})} \]

4. **Calculate the Pressure**:
- First, calculate the numerator:
\[ 2 \times (1.52 \times 10^4) = 3.04 \times 10^4 \]
- Now calculate the denominator:
\[ 3 \times (20 \times 10^{-6}) = 60 \times 10^{-6} \]
- Now, divide the numerator by the denominator:
\[ P = \frac{3.04 \times 10^4}{60 \times 10^{-6}} = \frac{3.04 \times 10^4}{6 \times 10^{-5}} = \frac{3.04}{6} \times 10^{4 + 5} = 0.5067 \times 10^9 = 5.067 \times 10^6 \text{ N/m}^2 \]

5. **Final Result**:
- The pressure of hydrogen in the cylinder is approximately:
\[ P \approx 5 \times 10^6 \text{ N/m}^2 \]

### Final Answer:
The pressure of hydrogen in the cylinder is \( 5 \times 10^6 \) N/m².