A system goes from state 1 to state 2 and back to state 1 following a reversible path in both directions. Which of the following statements about this process is or are true?
c. The value of w on going from state 1 to state 2 is equal in magnitude and opposite in sign to the value of w on going from state 2 back to state 1.

Verified step by step guidance

1. Identify that the process described is a reversible cycle, meaning the system returns to its initial state.
2. Recall that in a reversible process, the work done (w) is path-dependent but the net change in state functions like internal energy (U) is zero over a complete cycle.
3. Understand that for a reversible cycle, the work done from state 1 to state 2 (w_1→2) and the work done from state 2 back to state 1 (w_2→1) must sum to zero because the system returns to its original state.
4. Express this mathematically as w_1→2 + w_2→1 = 0, which implies that w_1→2 = -w_2→1.
5. Conclude that the statement is true: the work done from state 1 to state 2 is equal in magnitude and opposite in sign to the work done from state 2 back to state 1.

Key Concepts

Reversible Processes

A reversible process is a thermodynamic process that can be reversed without leaving any trace on the surroundings. In such processes, the system and surroundings can be returned to their original states. This concept is crucial for understanding how energy and work are exchanged in a system, as it implies that the system can undergo changes in a controlled manner, allowing for the analysis of work done in both directions.

Work in Thermodynamics

In thermodynamics, work (denoted as 'w') is defined as the energy transferred when a force is applied over a distance. The sign of work is important: work done by the system on the surroundings is considered negative, while work done on the system is positive. Understanding this concept is essential for analyzing energy changes during reversible processes, particularly in determining the relationship between work done in both directions of a reversible path.

First Law of Thermodynamics

The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another. This principle implies that the total energy change in a system is equal to the heat added to the system minus the work done by the system. In the context of reversible processes, this law helps to establish the relationship between the work done in both directions, reinforcing the idea that the work done going from state 1 to state 2 is equal in magnitude and opposite in sign to that going back.