Question

Which of the following is correct for adiabatic free expansion against vacuum?

• A. q=0, ΔU=0, w=0
• B. q≠0, w≠0, ΔU=0
• C. q=0, ΔU≠0, w≠0
• D. q=0, ΔU≠ 0, w≠0

Answer 1

The Correct Option is A

 To understand the situation of adiabatic free expansion against a vacuum, let's go through the thermodynamic principles step-by-step.

1. \(Adiabatic\ Process:\) An adiabatic process is one in which there is no heat exchange between the system and its surroundings. Hence, \(q = 0\).
2. \(Free\ Expansion:\) In a free expansion process, the system expands into a vacuum without any external pressure acting on it. Therefore, no work is done on or by the system. Hence, \(w = 0\).
3. \(First\ Law\ of\ Thermodynamics:\) The first law states that the change in internal energy of the system is equal to the heat added to the system minus the work done by the system. Mathematically, it can be expressed as: \(\Delta U = q - w\). Given \(q = 0\) and \(w = 0\), it follows that \(\Delta U = 0\).

Thus, in an adiabatic free expansion of gas into a vacuum, there is no heat exchange, no work is done, and the change in internal energy is zero.

Therefore, the correct option is q=0, ΔU=0, w=0.

Process	Heat Exchange (q)	Work Done (w)	Change in Internal Energy (ΔU)
Adiabatic Free Expansion	\(q = 0\)	\(w = 0\)	\(\Delta U = 0\)

This succinctly explains why the internal energy remains unchanged, and the work and heat exchange are zero during adiabatic free expansion into a vacuum. This concept is commonly tested in physics and chemistry exams and is an important principle in thermodynamics.