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Chapter 12: Problem 28

The internal energy \(U\) is a unique function of any state because of change in \(U\) (A) does not depend upon path. (B) depends upon path. (C) corresponds to an adiabatic process. (D) corresponds to an isothermal process.

Short Answer

Expert verified
The internal energy (U) is a unique function of any state because the change in U does not depend upon path. This property makes internal energy a state function, which means it depends only on the current state of the system and not on the path taken to reach that state. Therefore, the correct answer is Option A.

Step by step solution

01

Understanding Internal Energy

Internal energy (U) is a property of a system that depends on the state variables like temperature, pressure, and volume. It is a measure of the total kinetic and potential energy of the molecules in a system and is a state function, meaning it depends only on the current state of the system and not on the path taken to reach that state. Now, let's analyze each option:
02

Option A

The change in internal energy does not depend upon the path. This statement is consistent with the property of state functions. Since internal energy is a state function, the change in internal energy between two states is independent of the path taken to reach the final state from the initial state.
03

Option B

The change in internal energy depends upon the path. This statement contradicts the property of state functions. As mentioned earlier, internal energy is a state function and does not depend on the path taken to reach a particular state.
04

Option C

The change in internal energy corresponds to an adiabatic process. An adiabatic process is a thermodynamic process in which no heat is exchanged between the system and its surroundings. However, it does not explain why internal energy is a unique function of any state.
05

Option D

The change in internal energy corresponds to an isothermal process. Isothermal processes occur at a constant temperature, which means the internal energy might not change if the process is ideal. However, this does not explain why internal energy is a unique function of any state. By analyzing each option, we find that:
06

Conclusion

Option A, which states that the change in internal energy does not depend upon path, is the correct answer. This property explains why internal energy is a unique function of any state as it is a state function.

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