Two litres of an ideal gas at a pressure of 10 atm expands isothermally into vacuum until its volume is 10 litres. How much work is done in expansion ?

Question

Accepted Answer

To determine the work done during the isothermal expansion of an ideal gas into a vacuum, we need to consider the nature of the process. The expansion into a vacuum is known as a free expansion. In a free expansion, the gas expands without any external pressure opposing it, meaning there is no work done by or on the system.

1. **Explanation for Option 4 (0 L. atm):**
   - In thermodynamics, work done by a gas during expansion is calculated using the formula $ W = P \Delta V $, where $ P $ is the external pressure and $ \Delta V $ is the change in volume. However, in a free expansion, the external pressure $ P $ is zero because the gas is expanding into a vacuum. Therefore, the work done $ W = 0 \times \Delta V = 0 $.
   - Since no external force is applied to contain the gas, and it expands freely, no energy is transferred as work. Thus, the correct answer is Option 4, which states that the work done is 0 L. atm.

2. **Explanation for why other options are incorrect:**
   - **Option 1 (8 L. atm):** This option suggests that some work is done during the expansion. However, since the expansion is into a vacuum, there is no opposing pressure, and thus no work is done. Therefore, this option is incorrect.
   - **Option 2 (10 L. atm):** Similar to Option 1, this option implies that work is done. Again, because the expansion occurs into a vacuum, the external pressure is zero, resulting in zero work done. Hence, this option is incorrect.
   - **Option 3 (80 L. atm):** This option suggests a significant amount of work is done, which is not possible in a free expansion into a vacuum. The absence of external pressure means no work is performed, making this option incorrect.

In conclusion, the correct answer is Option 4, as no work is done during the isothermal expansion of an ideal gas into a vacuum.