Choose all of the processes from below which describe changes which are independent of the path by which the change occurs.

Question: Choose all of the processes from below which describe changes which are independent of the path by which the change occurs.

The following processes are independent of the path by which the change occurs:

• Change in internal energy
• Change in enthalpy
• Change in entropy
• Change in free energy
• Change in Gibbs free energy

These processes are all state functions, which means that their values depend only on the initial and final states of the system, not on the path taken between those states.

For example, the change in internal energy of a system is given by the equation:

ΔU = Q - W

where ΔU is the change in internal energy, Q is the heat transferred to the system, and W is the work done by the system.

The change in internal energy is independent of the path taken between the initial and final states because the heat transferred to the system and the work done by the system are path-dependent. However, the difference between the heat transferred to the system and the work done by the system, which is the change in internal energy, is independent of the path.

The other processes listed above are all state functions, so they are all independent of the path taken between the initial and final states.

Here are some examples of processes that are not independent of the path by which the change occurs:

• The distance traveled by a car between two points
• The amount of time it takes to travel between two points
• The amount of work done to lift an object to a certain height

These processes are all path-dependent, meaning that their values depend on the path taken between the initial and final states.

For example, the distance traveled by a car between two points can vary depending on the route taken. The amount of time it takes to travel between two points can also vary depending on the route taken, as well as the traffic conditions. And the amount of work done to lift an object to a certain height can vary depending on the path taken.

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