Today’s lesson may seem mundane; despite its subtlety, it is actually quite important. I needed to spend some time to learn it and digest it, and it was time well spent – these concepts are essential for understanding much of thermodynamics. For brevity, I have not dived into the detailed mathematics of exact differentials, though I highly recommend you to learn it and review the necessary calculus.

Some thermodynamic properties of a system can be described by **state variables**, while others can be described by **path variables**.

A **state variable** is a variable that depends only on the final and initial states of a system and not on the path connecting these states. Internal energy and enthalpy are examples of state functions. For example, in a previous post on the First Law of Thermodynamics, I defined the **change in internal energy**, , as

.

State variables can be calculated by exact differentials.

A **path variable** is a variable that depends on the sequence of steps that takes the system from the initial state to the final state. This sequence of steps is called the **path**. Heat and work are examples of path variables. Path variables *cannot* be calculated by exact differentials. In fact, the following quantities may seem to have plausible interpretations, but they actually** do not exist:**

- change in heat ()
- initial heat ()
- final heat ()
- change in work ()
- initial work ()
- final work ()

**There is no such thing as heat or work being possessed by a system. **Heat and work can be transferred between the system and the surroundings, but the end result is an increase or decrease in internal energy; neither the system or the surroundings possesses heat or work.

A state/path variable is also often called a state/path function or a state/path quantity.

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