# 2.3: Conservation

$$\newcommand{\vecs}{\overset { \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}{\| #1 \|}$$ $$\newcommand{\inner}{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}{\| #1 \|}$$ $$\newcommand{\inner}{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$

The last idea to be introduced in this chapter is the concept of conservation. In this course, a conserved property cannot be generated or consumed (created or destroyed). This is short and simple but represents a very, very powerful idea. When applied to the accounting concept, it means that all of the generation and consumption terms are identically equal to zero.

You should be aware of the fact that not everyone uses this definition for conservation. Most physics textbooks use the word "conserved" to indicate that there is no change in the amount of the conserved quantity inside the system. For example, conservation of momentum in most physics books is a principle that is only used to consider systems in which the momentum of the system is a constant. This approach uses "conserved" as a modeling assumption that may or may not hold for a given problem. In this course, we will always use "conserved" as a statement about a fundamental physical law. In our usage the concept of conservation relates to how the world works in general.

It turns out that most of the important fundamental laws in physics are Conservation Laws — mass, charge, linear momentum, angular momentum, and energy. The remaining law we will consider is the Second Law of Thermodynamics. It can be represented by an accounting principle where entropy can never by consumed.

We can write Accounting Statements or Accounting Equations for any extensive property. However, we can only write Conservation Laws or Conservation Equations for selected extensive properties. The validity of these laws is then based on accumulated empirical evidence that certain selected extensive properties are conserved.

## Test Yourself

1. Are you sure you know what "net" means? Revisit Equation $$2.2.2$$ and rewrite it in terms of two new net terms — $$\dot{B}_{out, net}$$ and $$\dot{B}_{cons, net}$$.
2. Revisit Equation $$2.2.1$$. How would this equation simplify if you assumed that the system in question was isolated? What if it was operating under steady-state conditions?
3. Write an equation similar to Equation $$2.2.1$$ that would be correct for a conserved property — a conservation law.
4. Now revisit the balloon problem. What do you think would be the best system? What properties should you count? What form of the accounting concept would be the best place to start out?

This page titled 2.3: Conservation is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Donald E. Richards (Rose-Hulman Scholar) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.