# Are energy and work the same thing?

When revising formulas the other day I came across something:

Energy = power × time

If we substitute power we get

Energy = work/time × time

The time cancels out. So is work equal to energy?

• Work is one way to change the energy of a system. Work can equal the product of power and time; so can the energy delivered to a system, and so can the change in energy of a system. This is how these concepts fit together. I think you could have answered this yourself by looking up the definitions of work and energy. Aug 23, 2021 at 22:59
• Nick Lucid has said on his YouTube channel Science Asylum that "Energy is the amount of stuff that can happen. Work is the amount of stuff that happens." Which is very loose and imprecise in its language, at least outside of context, but I don't think it's incorrect. Aug 24, 2021 at 15:04
• An analogy: if energy is the amount of money you have then work is a transaction. Using transactions you can exchange money between people. Using work you can exchange energy between objects. Energy and work both have the same units similar to how money and transactions are both measured using the same currency (like dollars or euros). Aug 24, 2021 at 17:30
• See also Newton's second law: $\sum\vec F = m\vec a$, but $m\vec a$ is not a force. Aug 24, 2021 at 19:41
• Interestingly, in greek, "energy" means "the thing that has work inside". Aug 24, 2021 at 20:25

Are energy and work the same thing

No.

Work is one of the two means for transferring energy. The other is heat. But work (and heat) are not the energy itself. They are processes for transferring energy.

The energy transferred by work or heat results in an increase or decrease in the internal energy of the entities that transfer the energy between them.

Hope this helps.

• Is there another way too? Not sure. Seems like chemical reactions and decay or nuclear reactions could be seen to transfer energy from or to something Aug 24, 2021 at 3:47
• I believe the underlying energy transfer mechanisms involved with chemical and nuclear reactions are still heat and work. An exothermic reaction gives off heat. An endothermic reaction absorbs heat. An exothermic reaction (combustion) in the confines of a cylinder fitted with a movable piston produces work. Aug 24, 2021 at 6:06
• Heat transfer and work don't really differ much when looked at a micro level. It is the statistics that makes them different - heat is chaotic, work is organized. Aug 24, 2021 at 9:24
• @fraxinus Viewing collisions at the molecular level, I agree. But at the macroscopic level the distinction is quite clear. It’s why the transfer of random molecular kinetic energy from a hot object to a cold object (heat) doesn’t cause motion of the cold object, whereas the transfer of the organized molecular kinetic energy of an object in motion upon colliding with a stationary object (work) does cause motion of the stationary object. Aug 24, 2021 at 12:39
• @BCLC Yes. The impulse of force is defined as Impulse=$F_{ave}\Delta t$ where $F_{ave}$ is the average force and $\Delta t$ is the time it is exerted. Then, combining that with Newton’s second law $F_{ave}=ma_{ave}=m\frac{\Delta v}{\Delta t}$ we have Impulse = $F_{ave}\Delta t=m\Delta v$ which is the change in momentum assuming constant mass. We can also look at this from the work energy principle where $F_{ave}d=-mv^{2}/2$. Aug 25, 2021 at 16:16

Work is a transfer of energy. So they are closely related (including the same units) but they are not the same.

• Specifically the change (transfer) of energy by way of force? (As opposed to heat). Aug 24, 2021 at 3:45
• Work is a change in energy, not any change in energy. Work, as defined by modern textbooks, includes transfer of energy by fields, not just forces. It only excludes energy transferred by heat. However, if I were to be given a magic wand to rewrite textbooks then I would indeed have work be any change in energy and then heat would simply be thermal work.
– Dale
Aug 24, 2021 at 11:36

Work as well as heat are means of energy transfer. While you may have (or carry og contain) energy, e.g. thermal energy or kinetic energy etc., you can't "have" work nor heat.

• Heat is what we call thermodynamic energy transfer (miniscule vibrations passed on from particle to particle).
• Work is what we call mechanical energy transfer (larger displacements or volume changes due to mechanical forces).

So, saying that "work is energy" sounds slightly off in engineering ears. Rather, work is specifically "energy in transit", so to say.

Power is a term invented for energy-transferred-per-time. This could pop up in many scenarios. When you heat up water for spaghetti cooking, the transferred energy is heat, so the power might be defined as heat-per-time, $$P=\frac Qt.$$ When you run a car engine where pistons within the engine chambers compress and extend fuel gas, then the power might more usefully be defined as work-per-time, $$P=\frac Wt.$$ Bottom line, I usually always just write power as: $$P=\frac Et$$ (or possibly as $$P=\Delta E/t$$ to indicate that we are dealing with a change in energy) before I know which scenario to apply it to and which energy-transfer mechanism that is involved. Then your small equation rearrangement would simply be:

$$\text{energy}=\text{power}\cdot\text{time}=\frac{\text{energy}}{\text{time}}\cdot \text{time}\quad\Leftrightarrow \\ \text{energy}=\text{energy}.$$

• To get it correct, you should have your "bottom line" as $P = \frac {\Delta E} t$. Aug 24, 2021 at 9:22
• @Džuris Wouldn't you then also prefer $\Delta t$ in the denominator? Aug 24, 2021 at 9:25
• I don't think it's as important in this case and $t$ can be a good enough symbol for a duration. But there are plenty of times where we have some energy "stored" in the system. E.g. if you accelerate a cart that was already moving, the power increases it's kinetic energy and it's $E=E_0 + Pt$ not $E=Pt$ . Aug 24, 2021 at 9:40
• @Džuris Thank you, I see your point. I am implicitly defining $E$ as energy transfered in this answer, but I might consider adjusting the symbol if it is confusing. Aug 24, 2021 at 9:52

Work is close to being energy. Notice that both have the same units, Joules. Now, specifically speaking, work is the amount of energy transferred to an object through a force over a distance. $$\text{Work} = F\cdot d\cdot\cos\theta$$ where $$F =$$ force applied to object, $$d =$$ displacement which object undergoes and $$\theta$$ is the angle between force and displacement vectors.

Note that what you get from algebra does not always reflect what you get in theory.

• Are there any other examples of essentially different physical quantities with identical dimensions? Aug 24, 2021 at 17:04
• @მამუკაჯიბლაძე Torque and work for instance, Nm. If you multiply torque by the dimensionless angle in radians that it turns, you get the work done. Aug 25, 2021 at 5:34
• @Neil_UK Thank you! Some more? :) Aug 25, 2021 at 6:57

Yes and no, depending on what we are talking about.

Statistical physics
E.g., in statistical physics we will refer to work and heat as the means of changing the internal energy of the system $$dU=dQ -dA$$ Clearly, here work is the change of energy. Moreover, it is not the full change, if the heat transfer is also present.

Mechanics
In mechanics work is the product of the force and displacement $$\mathbf{F}\cdot\mathbf{d}$$. This does not necessarily change the energy of the system, since there may be another force doing the opposite work. In other cases it may transform energy from one form to another (e.g., kinetic energy into potential and vice versa). Finally, in non-conservative systems, it may indeed change the total energy, as in the case of friction.

Potential energy is work
Finally, it is not uncommon to encounter statements such as

potential energy is work required to assemble the system (or bring a charge from infinitely far)

Note that this still could be interpreted as a change in the potential energy.

Energy = power × time

No, it's not. The correct statement (assuming constant power or "the average" power) would be:

Energy change during a time period = power × time

Your other substitution is only correct if you are considering a process where the energy is only changed by work. In such processes it is indeed accurate to do that substitution and say:

Energy change = work

But in general the energy could also be changed via heat, so it's

Energy change (of a system) = work (done on the system) + heat (supplied to the system)

And that's the first law of thermodynamics. The clarifications in parentheses are crucial because they change the sign of the term. E.g. work done on the system increses it's energy, but if you'd consider work done by the system, it would spend and thus decrease the system's energy.

Energy is the capability of a body to make work, determined by the state of the body. For example, a ball on the top of a tower can make work falling down by its position in the gravitational field of the Earth (potential energy). A bullet can penetrate a tree by its kinematic state (kinematic energy). Generally, the energy type tells about which particular aspect of the body state confers energy to the body. Energy and work share the same physical dimensions but they are not the same thing.

No, it's not the same. You need to perform Work to change Energy.

Eg. You need to lift a 10 kg object 2 metres from the ground:

Potential Energy of object at Ground Level = m x g x h = 10 kg x 9.81 x 0m = 0J

Work performed = Force x distance = 10kg x 9.81 x 2m = 98.1N x 2m = 196.2 N.m

Potential Energy of object at 2m above Ground Level = 10 kg x 9.81 x 2m = 196.2 J

Energy is something a physical system has; work is something done to or done by physical systems.

## Work-energy theorem

The work-energy theorem explains the idea that the net work - the total work done by all the forces combined - done on an object is equal to the change in the kinetic energy of the object.

Here's a simple example that I think is useful for the basic concept of this relationship:

Imagine you have a 1kg weight and you carry it up a hill to a height of 100 meters.

We can calculate that the gravitational potential energy of the the weight has increased by 980J. Q: Where did that increase come from? A: When you carried it up the hill you did at least 980J of work. In order to do that, you must have used (at least) 980J of energy. I like to think (simplified and informally) of work as the application of energy. This image represent how we earn money and spend also.

With physical example we understand better than a theoretical example.

Money is like energy we earn this by work . Work and energy has same unit but how different is clearly shown in figure . Work is just a way to transfer energy , as work is just a way to get money and transfer this to get things.

• This answer might be better if it explained the analogy... What is represented by "energy" in this image? What is represented by "work" in this image? As OP observed, work and energy have the same units. Both are money here? Is "Energy" your net worth, and "work" your income? And the first picture tries to say that you should let your money work for you, and not work for your money. Does that mean anything for energy? I understand the difference between work and energy, but I really don't understand how this analogy should work... Aug 24, 2021 at 12:07