Explanation:
The change in internal energy (dU) of a system can be expressed in terms of temperature (T), entropy (S), pressure (p), and volume (V) using the first law of thermodynamics. The first law of thermodynamics states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system.

The equation for the change in internal energy (dU) is given by:

dU = Q - W

where Q is the heat added to the system and W is the work done by the system.

Key Points:
- dU represents the change in internal energy of the system.
- T represents temperature.
- S represents entropy.
- p represents pressure.
- V represents volume.

Given:
The composition of the system does not change.

Explanation:
The composition of a system refers to the types and amounts of substances present in the system. If the composition of the system does not change, it means that there is no transfer of matter into or out of the system. In other words, the number of particles and the types of particles remain constant.

When the composition of the system does not change, it implies that there is no heat added to or removed from the system, and no work is done by or on the system. Therefore, the first law of thermodynamics simplifies to:

dU = 0

Since there is no change in internal energy (dU = 0), the equation can be rearranged to:

0 = TdS - pdV

Thus, the statement "dU = TdS - pdV" is true when the composition of the system does not change. This equation is known as the fundamental equation of thermodynamics and is a mathematical representation of the first law of thermodynamics.

Conclusion:
Therefore, the correct answer is option A) true. When the composition of the system does not change, the equation dU = TdS - pdV holds true.