# If the first law of thermodynamics ensures conservation of energy, why does it allow systems to lose energy?

I am learning the basics of Thermodynamics.

Everywhere I read about the first law, it states "conservation of energy", and talks about how change in internal energy equals heat and work transfer.

I am aware of work transfer being considered positive and negative depending on the point of view we want to set.

That is okay.

But it confuses me to see the word "conservation".

If we take a very simple or at least very common real process like putting a plastic bottle completely filled with liquid water into a freezer (or whatever environment that is constantly under 273 K) and wait for thermal equilibrium to happen, the bottle will have expanded because water will have frozen increasing its volume and pushing the bottle's limits.

In this case:

The system (the bottle) has lost or given away a whatever amount of heat and it will also have generated a work transfer (to make the bottle expand).

It doesn't matter if we consider that work positive once or negative twice, in both cases energy has left the system in the form of work.

The total amount of internal energy of the system has clearly decreased.

So apparently there isn't really any "conservation" happening.

I do not intend to hate on thermodynamics, it's actually beautiful, I just want to understand the semantics.

I read other similar questions like this one, but in none did I find a clear answer.

• In your example, the system would have to be the bottle AND the freezer, and the conservation of energy would imply that whatever heat was lost by the bottle must have been absorbed by the freezer. In general you want to consider closed systems, i.e. systems which do not interact with the environment (as the bottle taken alone is doing with the freezer).
– Pxx
Aug 20, 2019 at 22:28
• "conservation of energy", and talks about how internal energy equals heat and work transfer. This is wrong. It should be change in internal energy. Aug 20, 2019 at 22:52
• Reminder: Answers go in the answers, not in comments. This is not directed at any one comment. Aug 21, 2019 at 15:55
• Not really related to your question, but worth noting. Cold makes things contract not expand. The reason the bottle expands is because of the lattice structure that is created when water freezes. Aug 22, 2019 at 14:35

“Conserved” doesn’t mean “never changes”. It means “this stuff is real, and the only way you have less or more is if some is taken away or added”. You can then follow that additions or subtractions.

Since your cold bottle has less energy, the conservation law says that energy has not disappeared, it’s just gone somewhere. You can find it. You can figure out how it got there.

I'm not sure why people are saying this only applies to closed systems. This law actually applies to all systems. The first law is conservation of energy. It says the change in energy is equal to the energy that enters/leaves it in the form of work or heat. i.e. $$\Delta U=W+Q$$ where $$U$$ is the internal energy, $$W$$ is the work done on the system, and $$Q$$ is the heat that enters the system. This equation essentially just says we can track where the energy of our system is coming from/going to. It isn't suddenly appearing from or disappearing to some "unknown nowhere". It's energy conservation.

In your system, heat left the system, and the system did some work on the environment I suppose (though this might be negligible). In any case, $$Q<0$$ and $$W<0$$, so it should be no surprise that $$\Delta U<0$$. Energy has left your system (and has gone somewhere else), so the internal energy has decreased. Energy conservation is true, and it's present in the first law here.

• In engineering, a closed system is one in which no mass enters of leaves, but one which can exchange of heat and work with the surroundings. What you are envisioning as a closed system is what we call an "isolated system." Aug 20, 2019 at 23:41
• @ChetMiller Ah ok, thanks. I have removed my parenthetical comment. In any case, the first law still applies to all systems. Aug 20, 2019 at 23:44
• I accepted Bob Jacobsen's answer because it goes straight to the semantics and makes it clear at one shot. Chet Miller's comment under the original question also did. I still appreciate your answer and it also helps. The combination of both should be the final one. All the best and thanks again. Aug 21, 2019 at 7:24
• @AlvaroFranz Glad I could help Aug 21, 2019 at 10:33

Conserved here doesn't mean that it is conserved only for your system (Not unless it's an isolated system). It is conserved for the whole universe. The total energy is constant. In performing any work or task , all you are doing is taking some energy from the surrounding and giving it to the system or vice versa. These 2 effects balance out or cancel each other if you consider the whole universe making thermodynamics "Perfectly balanced, as all things should be"

When it is said conservation of energy it's referred to the conservation of the energy on a closed system.

In your example, you're considering the bottle of water as that system, but the energy lost by the water and bottle due to cooling, phase change, and expansion is given as heat to the refrigerator. Furthermore, the refrigerator is in a constant energy exchange with the environment. So that's not a closed system.

As some already commented, the conservation stands for the fact that energy just transforms and you can find where it went.

The conservation of energy states that energy (its amount, not its form) is conserved, ie is not changed, in isolated systems.

I think your confusion stems from the slight difference of the 1st law of thermodynamics vs the conservation of energy. Quoting you, the law states "change in internal energy equals heat and work transfer". The word "conservation" is not in there, and you should not expect conservation if you are thinking in terms of the 1st law.

You could expect conservation if you made an isolated system which includes the freezer. Then, whatever heat the bottle lost and whatever work it did, would be the heat the freezer gained and the work it received. Total energy was conserved.