Which of the following is incorrect regarding the first law of thermodynamics?

The first law of thermodynamics states that the net heat supplied to a system, $$q$$, is equal to the change in its internal energy, $$\Delta U$$, plus the work done by the system, $$w$$:

$$q = \Delta U + w \quad -(1)$$

This law is, in effect, the application of the principle of conservation of energy to thermodynamic systems. Let us examine each option in this light.

Option A: “It is applicable to any cyclic process.”
During a complete cycle the initial and final states are identical, so $$\Delta U = 0$$. Equation $$-(1)$$ then gives $$q = w$$ for the whole cycle. Hence the first law is indeed valid for every cyclic process. Option A is correct.

Option B: “It is a restatement of the principle of conservation of energy.”
Equation $$-(1)$$ directly expresses energy conservation: the energy entering the system as heat either remains stored as internal energy or leaves as work. Therefore Option B is correct.

Option C: “It introduces the concept of the internal energy.”
Before thermodynamics, internal energy was not treated explicitly. The first law defines $$\Delta U$$ as a state function whose change balances heat and work. Hence Option C is correct.

Option D: “It introduces the concept of the entropy.”
Entropy $$S$$ appears only in the second law of thermodynamics and is not mentioned in the first law. Therefore Option D is an incorrect statement about the first law.

Thus the statement that is incorrect is:
Option D which is: It introduces the concept of the entropy