Question

$\Delta U $ is equal to :

• A. Adiabatic work
• B. Isothermal work
• C. Isochoric work
• D. Isobaric work

Answer 1

The Correct Option is A

The question pertains to the first law of thermodynamics, which is a fundamental principle in thermodynamics and chemistry. The first law states that the change in internal energy (\(\Delta U\)) of a system is equal to the heat added to the system minus the work done by the system on its surroundings. Mathematically, this is expressed as:

\(\Delta U = Q - W\)

Where:

• \(\Delta U\) = Change in internal energy
• \(Q\) = Heat added to the system
• \(W\) = Work done by the system

In an adiabatic process, there is no heat exchange between the system and its surroundings, meaning \(Q = 0\). Thus, the change in internal energy is due solely to the work done on or by the system.

Therefore, for an adiabatic process:

\(\Delta U = -W\)

This equation shows that the change in internal energy for an adiabatic process is numerically equal to the work done. Hence, \(\Delta U\) is equal to the adiabatic work, making this the correct answer.

Let’s justify why the other options are incorrect:

• Isothermal work: In an isothermal process, the temperature remains constant, and the internal energy change is zero for an ideal gas. Thus, \(\Delta U \neq Q - W\).
• Isochoric work: In an isochoric process, the volume remains constant, hence no work is done (\(W = 0\)), and \(\Delta U = Q\).
• Isobaric work: In an isobaric process, the pressure remains constant, but \(\Delta U\) is not equal to the work done since heat is also exchanged.

Thus, the only option that satisfies \(\Delta U\) is equal to the work done is the adiabatic work.