How to define "energy" and "work" without using either word

[brawler234]

I understand that work is done when (a) a force displaces an object, (b) energy is converted from one form to another, (c) heat is transferred between a system and its surroundings, yet I have trouble giving a precise definition for it.

Everywhere I go, the definition of energy is "the ability to do work" while the definition of work is "the transfer of energy."

How can we define energy without using the word "work" and vice versa?

 

[PeroK]

I understand that work is done when (a) a force displaces an object, (b) energy is converted from one form to another, (c) heat is transferred between a system and its surroundings, yet I have trouble giving a precise definition for it.

Everywhere I go, the definition of energy is "the ability to do work" while the definition of work is "the transfer of energy."

How can we define energy without using the word "work" and vice versa?

It's not easy to define energy in general. You can define kinetic energy, potential energy and then total mechanical energy specifically as KE + PE.

Then you can define thermal energy, chemical energy, nuclear energy.

I'd agree that the definition of energy as "the ability to do work" is woolly and can lead to circular arguments.

There's an amusing and educational video here:

 

[Dale]

Everywhere I go, the definition of energy is "the ability to do work" while the definition of work is "the transfer of energy."

This is not quite right. In different branches of physics there are different definitions for the same word. Usually the two definitions are equivalent under some circumstances, but each definition is tailored for the particular branch of physics where it is defined. Here you are mixing the definition of energy from mechanics with the definition of work from thermodynamics.

In mechanics work is defined as $\int F \cdot ds$. And energy is defined as the ability to do work. Everything is straightforward. Work is defined first in terms of fundamental concepts and then energy is defined based on work.

In thermodynamics kinetic energy is usually defined first as $\frac{1}{2} m v^2$ and then energy in general is defined as anything with the same units that can be converted to kinetic energy. Then work is defined as a transfer of energy. Again, everything is straightforward, but the order of definition is reversed.

So the confusion only arises when you take the second definition from each branch of physics. Note that if you are mixing branches then you could take the first definition from each branch and have each defined independently. Then you could derive both of the second definitions. In the end you wind up with the same four statements. As long as it is self consistent the order of definition and derivation is not particularly important.