Question

When the expansion of a gas occurs in vacuum and at constant volume, then:

• A. \( \Delta U = qV \)
• B. \( \Delta U = qp \)
• C. \( \Delta H = qV \)
• D. \( \Delta H = qp \)

Hint:

In an expansion at constant volume and in a vacuum, no work is done. Hence, the change in internal energy is equal to the heat added to the system.

Answer 1

The Correct Option is A

In thermodynamics, the first law is given by: \[ \Delta U = Q - W \] Where:
- \( \Delta U \) is the change in internal energy,
- \( Q \) is the heat added to the system,
- \( W \) is the work done by the system.
For a gas expansion in a vacuum, the work done \( W \) is zero because there is no external force against which the gas does work. Therefore, the first law of thermodynamics simplifies to: \[ \Delta U = Q \] Now, considering that the gas is expanding at constant volume, the heat added to the system \( Q \) is proportional to the change in internal energy, and we use \( Q = qV \), where \( qV \) is the heat absorbed at constant volume. Thus, the change in internal energy is: \[ \Delta U = qV \] Therefore, the correct answer is option (A).