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

Answer

To find the work done during the compression of a gas, we can use the formula:

\[ W = -P \Delta V \]

where:
- \( W \) is the work done,
- \( P \) is the pressure,
- \( \Delta V \) is the change in volume.

### Step 1: Identify the given values
- Pressure \( P = 100 \, \text{kPa} = 100 \times 10^3 \, \text{Pa} \)
- Initial volume \( V_i = 1 \, \text{m}^3 \)
- Final volume \( V_f = 10 \, \text{dm}^3 \)

### Step 2: Convert the final volume to cubic meters
Since \( 1 \, \text{dm}^3 = 10^{-3} \, \text{m}^3 \), we can convert \( V_f \):
\[ V_f = 10 \, \text{dm}^3 = 10 \times 10^{-3} \, \text{m}^3 = 0.01 \, \text{m}^3 \]

### Step 3: Calculate the change in volume \( \Delta V \)
\[ \Delta V = V_f - V_i \]
\[ \Delta V = 0.01 \, \text{m}^3 - 1 \, \text{m}^3 = -0.99 \, \text{m}^3 \]

### Step 4: Substitute the values into the work done formula
Now we can substitute \( P \) and \( \Delta V \) into the work done formula:
\[ W = -P \Delta V \]
\[ W = - (100 \times 10^3 \, \text{Pa}) \times (-0.99 \, \text{m}^3) \]

### Step 5: Calculate the work done
\[ W = 100 \times 10^3 \times 0.99 \]
\[ W = 99000 \, \text{J} \]

Thus, the work done during the compression of the gas is:
\[ \boxed{99000 \, \text{J}} \]