Question

Three moles of an ideal gas expanded spontaneously into vaccum. The work done will be

• A. 3 Joules
• B. 9 Joules
• C. Zero
• D. Infinite

Answer 1

The Correct Option is C

To understand why the work done is zero, we need to discuss the concept of gas expansion in a vacuum. This process is known as "free expansion" and has some special properties.

In thermodynamics, work done W by or on a gas is given by the formula:

• W = P \cdot \Delta V

where P is the pressure and \Delta V is the change in volume.

For free expansion:

• The gas expands against a vacuum, meaning there is no external pressure (P = 0).
• As a result, using the formula for work, W = 0 \cdot \Delta V = 0.

This means no work is done during this expansion, regardless of the change in volume because there's no force exerted by the gas against an external pressure.

Conclusion: Since the process involves expansion into a vacuum, the work done for three moles of an ideal gas is Zero. Therefore, the correct answer is Zero, which means the other options are irrelevant in this context.