Cant grasp difference between infinitesimal change and macroscopic change

[Dars]

What does infinitesimal change in V mean? Can someone please illustrate with simple example.

Lecture notes say infinitesimal change in V = dV
And large change in V is delta V.. I don't understand what it means though

 

[chemisttree]

Infitesimal change is something like... change in volume = 0.0000000001L

large change is something like... change in volume = .5L

http://en.wikipedia.org/wiki/Infinitesimal"

 

[nismaratwork]

In the context of your textbook, was it just referring to magnitude or was it also using that as a way of saying, "change below the limit we need to be concerned with."?

 

[Vulgar]

I think this is more of a mathematical question, try and ask the question on the math board (calculus section).

It's like when you try and deduce the average speed of a car, when you know it traveled 10m in 2s, the average speed during those 2 seconds is 5m/s, and that's delta(x)/delta(t). If you want to know the exact speed at one particular moment in time, you need the function of x(t) and derive it, being dx/dt, so the infinitesimal change in position divided by the infinitesimal change in time.

 

[LudusRex]

Infinitesimal change refers to a very small or tiny change in a variable, while macroscopic change refers to a large or noticeable change in the same variable. In this case, the variable is volume (V).

To better understand the difference, let's look at an example. Imagine you have a glass of water that is almost full. If you add just a few drops of water to the glass, the volume of the water will increase by a very small amount. This is an infinitesimal change in volume (dV) because it is a very small change that is not easily noticeable.

On the other hand, if you were to pour a whole bottle of water into the glass, the volume of the water would increase significantly. This would be a macroscopic change in volume (delta V) because it is a large and noticeable change.

In scientific equations, infinitesimal changes are denoted by the symbol "d" (such as dV), while macroscopic changes are denoted by the symbol "delta" (such as delta V). These symbols help to differentiate between small and large changes in a variable.

It is important to understand the difference between infinitesimal and macroscopic changes, as they can have different effects on a system. In some cases, infinitesimal changes may be negligible and have no significant impact, while macroscopic changes can greatly affect the behavior or properties of a system.

I hope this explanation helps to clarify the concept of infinitesimal change in volume and its difference from macroscopic change.