Two litres of an ideal gas at a pressure of 10 atm expands isothermally against a constant external pressure of 1 atm until its total volume in 10 litres. The work done (-w) in the expansion is :

Question

Accepted Answer

To determine the work done (-w) during the isothermal expansion of an ideal gas, we can use the formula for work done against a constant external pressure:

$$ w = -P_{\text{ext}} \times \Delta V $$

where:
- $ P_{\text{ext}} $ is the constant external pressure,
- $ \Delta V $ is the change in volume.

Given:
- Initial volume ($ V_i $) = 2 litres
- Final volume ($ V_f $) = 10 litres
- External pressure ($ P_{\text{ext}} $) = 1 atm

First, calculate the change in volume ($ \Delta V $):

$$ \Delta V = V_f - V_i = 10 \, \text{litres} - 2 \, \text{litres} = 8 \, \text{litres} $$

Now, substitute the values into the work formula:

$$ w = -1 \, \text{atm} \times 8 \, \text{litres} = -8 \, \text{litre-atm} $$

The work done (-w) is therefore 8 litre-atm. Since work done on the system is considered negative, the work done by the system is positive, hence the work done (-w) is 8 litre-atm.

**Explanation for Option 3 being correct:**
- Option 3 states that the work done (-w) is 8 litre-atm, which matches our calculation. The process involves expansion against a constant external pressure, and the calculated work done aligns perfectly with this option.

**Explanation for why other options are incorrect:**
1. **Option 1 (0 litre-atm):** This would imply no work is done, which is incorrect because there is a change in volume against an external pressure.
2. **Option 2 (10 litre-atm):** This value does not match the calculated work done of 8 litre-atm. It suggests a different scenario or calculation error.
3. **Option 4 (1 litre-atm):** This is far less than the calculated work done and does not reflect the actual expansion work against the external pressure.

In conclusion, Option 3 is the correct answer as it accurately represents the work done during the isothermal expansion of the gas under the given conditions.