Find kinetic energy of 3 litre of a gas at S.T.P given standard pressure is `1.013 xx 10^(5) N//m^(2)`.

Answer

To find the kinetic energy of 3 liters of gas at standard temperature and pressure (STP), we can use the formula for the kinetic energy of a gas:

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

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

### Step 1: Convert Volume from Liters to Cubic Meters
Given that the volume of the gas is 3 liters, we need to convert this to cubic meters (SI unit).

\[ 1 \text{ liter} = 10^{-3} \text{ m}^3 \]

Thus,

\[ 3 \text{ liters} = 3 \times 10^{-3} \text{ m}^3 \]

### Step 2: Identify the Pressure
The pressure at STP is given as:

\[ P = 1.013 \times 10^5 \text{ N/m}^2 \]

### Step 3: Substitute Values into the Kinetic Energy Formula
Now we can substitute the values of \( P \) and \( V \) into the kinetic energy formula:

\[ KE = \frac{3}{2} \times (1.013 \times 10^5 \text{ N/m}^2) \times (3 \times 10^{-3} \text{ m}^3) \]

### Step 4: Calculate the Kinetic Energy
Calculating the above expression:

\[ KE = \frac{3}{2} \times 1.013 \times 10^5 \times 3 \times 10^{-3} \]

\[ = \frac{3}{2} \times 1.013 \times 3 \times 10^2 \]

\[ = \frac{3 \times 3.039}{2} \times 10^2 \]

\[ = 4.5585 \times 10^2 \text{ Joules} \]

\[ = 455.85 \text{ Joules} \]

### Final Answer
The kinetic energy of 3 liters of gas at STP is:

\[ \boxed{455.85 \text{ Joules}} \]

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