If a gas of volume 10 L is expanded to quadruple its volume at 4 atm pressure, the external work done is

Options

A. 3 kJ
B. 6 kJ
C. 12 kJ
D. 18 kJ

Answer

To solve the problem of calculating the external work done when a gas expands, we can follow these steps:

### Step 1: Understand the Given Information
We have the following information:
- Initial volume (V1) = 10 L
- Final volume (V2) = 4 * V1 = 4 * 10 L = 40 L
- Pressure (P) = 4 atm

### Step 2: Convert Units
Since we need to calculate work done in standard units, we should convert the pressure from atm to pascals (Pa).
1 atm = 101325 Pa, therefore:
\[ P = 4 \text{ atm} = 4 \times 101325 \text{ Pa} = 405300 \text{ Pa} \]

### Step 3: Use the Formula for Work Done
The work done (W) during an expansion at constant pressure can be calculated using the formula:
\[ W = P \Delta V \]
where \( \Delta V = V2 - V1 \).

### Step 4: Calculate the Change in Volume
Now, we can calculate the change in volume:
\[ \Delta V = V2 - V1 = 40 \text{ L} - 10 \text{ L} = 30 \text{ L} \]

### Step 5: Convert Volume to Cubic Meters
Since 1 L = 0.001 m³, we convert the volume change:
\[ \Delta V = 30 \text{ L} = 30 \times 0.001 \text{ m}³ = 0.03 \text{ m}³ \]

### Step 6: Calculate the Work Done
Now we can substitute the values into the work done formula:
\[ W = P \Delta V = 405300 \text{ Pa} \times 0.03 \text{ m}³ \]

### Step 7: Perform the Calculation
Calculating the above expression:
\[ W = 405300 \times 0.03 = 12159 \text{ J} \]

### Final Answer
The external work done is:
\[ W = 12159 \text{ J} \]

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