Where is the “conservation” in the first law of thermodynamics?ZzK89C Dns T Zz D D6x Y t
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.
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2$\\begingroup$ It's conservation of total energy, not just the system's energy. $\\endgroup$ – knzhou 9 hours ago
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$\\begingroup$ 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). $\\endgroup$ – Jxx 9 hours ago
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$\\begingroup$ "conservation of energy", and talks about how internal energy equals heat and work transfer. This is wrong. It should be change in internal energy. $\\endgroup$ – Aaron Stevens 9 hours ago
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2$\\begingroup$ This is an input - output = accumulation kind of thing. It's like a bank account, for which "conservation of money" exists. Deposits - Payments (checks) = change in bank balance. If money was disappearing, the FEDs would have to come in and arrest someone. In the first law, the change in internal energy is analogous to the change in bank balance. Heat added minus work done is analogous to deposits minus payments (although unlike a bank account, heat added and work done can both be positive or negative). $\\endgroup$ – Chet Miller 8 hours ago
3 Answers
“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.
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$\\begingroup$ 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." $\\endgroup$ – Chet Miller 8 hours ago
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$\\begingroup$ @ChetMiller Ah ok, thanks. I have removed my parenthetical comment. In any case, the first law still applies to all systems. $\\endgroup$ – Aaron Stevens 8 hours ago
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$\\begingroup$ 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. $\\endgroup$ – Alvaro Franz 56 mins ago
The energy of the water in the bottle has definitely decreased, but it's not a closed system. The freezer pumps the heat out, which heats up the external environment.
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$\\begingroup$ Good answer, but I think you should highlight the "closed system" part. This law applies to closed systems only. $\\endgroup$ – FGSUZ 9 hours ago
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$\\begingroup$ @FGSUZ I don't think that's true $\\endgroup$ – Aaron Stevens 8 hours ago