The pressure of a gas is 100 k Pa. if it is compressed from 1 `m^(3)` to `10 dm^(3)` , find the work done .

Options

A. `990 J`
B. 9990 J
C. 9900 J
D. 99000 J

Explanation

To solve the problem of calculating the work done when compressing a gas from an initial volume of 1 m³ to a final volume of 10 dm³ at a pressure of 100 kPa, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Pressure (P) = 100 kPa
- Initial Volume (V1) = 1 m³
- Final Volume (V2) = 10 dm³

2. **Convert Units:**
- Convert the final volume from dm³ to m³:
\[ V2 = 10 \, \text{dm}^3 = 10 \times 10^{-3} \, \text{m}^3 = 0.01 \, \text{m}^3 \]

3. **Use the Work Done Formula:**
- The work done (W) during compression can be calculated using the formula:
\[ W = -P \times (V2 - V1) \]
- Since we are compressing the gas, the work done on the system is considered positive, hence we can write:
\[ W = P \times (V1 - V2) \]

4. **Substitute the Values:**
- Convert pressure from kPa to Pa (1 kPa = 1000 Pa):
\[ P = 100 \, \text{kPa} = 100 \times 1000 \, \text{Pa} = 100000 \, \text{Pa} \]
- Now substitute the values into the formula:
\[ W = 100000 \, \text{Pa} \times (1 \, \text{m}^3 - 0.01 \, \text{m}^3) \]
\[ W = 100000 \, \text{Pa} \times (0.99 \, \text{m}^3) \]

5. **Calculate the Work Done:**
- Now perform the multiplication:
\[ W = 100000 \times 0.99 = 99000 \, \text{J} \]

6. **Final Answer:**
- The work done during the compression of the gas is:
\[ W = 99000 \, \text{J} \]