An ideal gas is allowed to expand from 1L to 10 L against a constant external pressure of 1 bar. The work doen in kJ is:

Options

A. `-9.0`
B. `+10.0`
C. `-0.9`
D. `-2.0`

Explanation

To solve the problem of calculating the work done when an ideal gas expands from 1L to 10L against a constant external pressure of 1 bar, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Initial Volume (V_initial) = 1 L
- Final Volume (V_final) = 10 L
- External Pressure (P_external) = 1 bar

2. **Convert the External Pressure to SI Units:**
- 1 bar = 1 × 10^5 Pascal (Pa)

3. **Convert the Volumes from Liters to Cubic Meters:**
- 1 L = 10^(-3) m³
- Therefore, V_initial = 1 L = 1 × 10^(-3) m³
- V_final = 10 L = 10 × 10^(-3) m³ = 0.01 m³

4. **Use the Work Done Formula:**
The work done (W) by the gas during expansion against a constant external pressure is given by:
\[ W = -P_{\text{external}} \times (V_{\text{final}} - V_{\text{initial}}) \]

5. **Substitute the Values into the Formula:**
\[ W = - (1 \times 10^5 \, \text{Pa}) \times (0.01 \, \text{m}^3 - 1 \times 10^{-3} \, \text{m}^3) \]
\[ W = - (1 \times 10^5) \times (0.01 - 0.001) \]
\[ W = - (1 \times 10^5) \times (0.009) \]
\[ W = - 900 \, \text{J} \]

6. **Convert the Work Done from Joules to Kilojoules:**
\[ W = -900 \, \text{J} = -0.9 \, \text{kJ} \]

### Final Answer:
The work done during the expansion is **-0.9 kJ**.

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