Exact differential

Imagine you have a toy car and you want to push it around. Sometimes, it's really easy to push it in a straight line and other times, it's a bit harder if there are bumps or obstacles in the way. In math, we call this "work", which measures how hard it is to move from one place to another.

Now let's pretend that the toy car represents a system, like a gas or a liquid. You can also think of this as a group of molecules moving around. Similarly, the path you push the toy car along represents a process that the system goes through, like heating it up or cooling it down.

Next, we want to talk about something called a differential. This is just a fancy word for a small change. So, when we say "exact differential", we mean that it's a very precise and specific change that happens to the system.

Think of it like taking your toy car and moving it just a tiny bit. If you move it by the same amount each time, you can measure exactly how much work you're doing to move it. This is an example of an exact differential because it's a very specific and precise change that you can measure consistently.

In math, an exact differential is a type of function that describes how a system changes based on different variables, like temperature or pressure. It means that the amount of work needed to move the system from one state to another depends only on the states themselves, and not on how you got there.

In summary, an exact differential is a very precise and specific change that happens to a system, and it helps us understand how the system changes based on different variables. Think of it like moving a toy car just a tiny bit, and measuring exactly how much work you're doing each time.