A cylinder of capacity `20 L` is filled with `H_(2)` gas. The total average kinetic energy of translatory motion of its molecules is `1,5 xx 10^(5) J`. The pressure of hydrogen in the cylinder is

Answer

To find the pressure of hydrogen gas in the cylinder, we can follow these steps:

### Step 1: Convert the volume from liters to cubic meters
The volume of the cylinder is given as 20 liters. We need to convert this to cubic meters (SI unit).

\[ \text{Volume (V)} = 20 \, \text{L} = 20 \times 10^{-3} \, \text{m}^3 = 0.02 \, \text{m}^3 \]

### Step 2: Use the formula for average kinetic energy
The total average kinetic energy (E) of the gas molecules is given as \(1.5 \times 10^5 \, \text{J}\). The relationship between the total kinetic energy and pressure can be expressed as:

\[ E = \frac{3}{2} PV \]

From this, we can rearrange to find pressure (P):

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

### Step 3: Substitute the values into the formula
Now we can substitute the values of E and V into the equation we derived for pressure.

\[ P = \frac{2 \times (1.5 \times 10^5 \, \text{J})}{3 \times (20 \times 10^{-3} \, \text{m}^3)} \]

### Step 4: Calculate the pressure
Now, we will perform the calculations step by step.

1. Calculate the numerator:
\[ 2 \times (1.5 \times 10^5) = 3.0 \times 10^5 \, \text{J} \]

2. Calculate the denominator:
\[ 3 \times (20 \times 10^{-3}) = 60 \times 10^{-3} = 0.06 \, \text{m}^3 \]

3. Now, divide the numerator by the denominator:
\[ P = \frac{3.0 \times 10^5}{0.06} = 5.0 \times 10^6 \, \text{N/m}^2 \]

### Step 5: Final result
Thus, the pressure of hydrogen in the cylinder is:

\[ P = 5.0 \times 10^6 \, \text{Pa} \, \text{(Pascals)} \]

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