The internal energy change when a system goes from state A to B is 40 kJ/mole. If the system goes from A to B by a reversible path and returns to state A by an irreversible path what would be the net change in internal energy?

To understand the change in internal energy when a system transitions between states, it's important to recognize a fundamental principle of thermodynamics: the internal energy of a system is a state function. This means that the change in internal energy depends only on the initial and final states of the system, not on the path taken to get there.

Internal Energy and State Functions

In thermodynamics, internal energy (U) is a measure of the total energy contained within a system. When a system transitions from one state to another, the change in internal energy (ΔU) can be calculated using the formula:

• ΔU = U_final - U_initial

Since internal energy is a state function, the path taken—whether reversible or irreversible—does not affect the overall change in internal energy between two states.

Analyzing the Given Scenario

In your case, the system transitions from state A to state B, resulting in a change of internal energy of 40 kJ/mole. This can be expressed as:

• ΔU (A to B) = 40 kJ/mole

Now, when the system returns from state B back to state A, regardless of whether this return path is reversible or irreversible, the change in internal energy will be:

• ΔU (B to A) = U_A - U_B = -ΔU (A to B) = -40 kJ/mole

Calculating the Net Change

To find the net change in internal energy for the entire process (A to B and then B to A), we can sum the changes:

• Net Change = ΔU (A to B) + ΔU (B to A)
• Net Change = 40 kJ/mole + (-40 kJ/mole)
• Net Change = 0 kJ/mole

Conclusion on Internal Energy Change

Thus, the net change in internal energy when the system goes from state A to B and then back to A, regardless of the paths taken, is zero. This illustrates the key concept that internal energy is dependent solely on the states involved, not the manner in which the transitions occur. Therefore, the answer to your question is that the net change in internal energy is 0 kJ/mole.