A gas expands from 10 litres to 20 litres against a constant external pressure of 10 atm. The pressure-volume work done by the system is

Options

A. 100 L atm
B. `-100` L atm
C. 10 L atm
D. `-10` L atm

Answer

To solve the problem of calculating the pressure-volume work done by the gas during its expansion, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Initial volume (V1) = 10 liters
- Final volume (V2) = 20 liters
- External pressure (P_external) = 10 atm

2. **Calculate the Change in Volume (ΔV):**
\[ \Delta V = V2 - V1 = 20 \, \text{liters} - 10 \, \text{liters} = 10 \, \text{liters} \]

3. **Use the Formula for Work Done (W):**
The formula for work done by the system during expansion is given by:
\[ W = -P_{\text{external}} \Delta V \]
Here, the negative sign indicates that work is done by the system (expansion).

4. **Substitute the Values into the Formula:**
\[ W = - (10 \, \text{atm}) \times (10 \, \text{liters}) = -100 \, \text{atm liters} \]

5. **Final Answer:**
The work done by the system during the expansion is:
\[ W = -100 \, \text{atm liters} \]