# First law of thermodynamics situation

1. Jan 27, 2010

### fluidistic

Hi,
My mind has been blown up recently when I came across this thread: https://www.physicsforums.com/showthread.php?t=372533.

I'd like some explanations about something.

Imagine an insulated tank filled with hydrogen and oxygen at 100°C (or greater if possible) and 1 atm.
Now a spark starts on.
Imagine that all the gas transformed into $$H_20$$. The temperature must increase as I've been told, so that the water is under the gas form (despite the fact that at higher pressure water needs to be put at more than 100°C).

From the first law of thermodynamics, I know that $$\Delta U = Q-W$$. In this case, Q and W are worth 0 J because no heat is exchanged within the surroundings of the system and the volume remains constant. So still according to the first law, $$\Delta U=0 J$$.
However, in Resnick-Halliday, it is clearly stated that the internal energy of a gas is directly proportional to its temperature and is only temperature dependent. Hence an increase of temperature means an increase of internal energy.
Hence according to this book, I'm tempted to say that the system has gained energy.
It is in contradiction with the first law.
What's going on?

Thanks a lot in advance, I really need to know!

2. Jan 27, 2010

### Matterwave

I think, in this case, you must use a more generalized form of the first law.

N changes in this reaction, so your first law must include the mu*dN term (where mu is the chemical potential, N is the number of particles). I'm not sure what else, but the form of the first law that you used makes a few assumptions on what parameters are changeable in your system (e.g. it assumes N stays constant, and perhaps some other stuff).

Last edited: Jan 28, 2010
3. Jan 28, 2010

### mikelepore

That's based on the assumption that internal energy is the sum of the kinetic energy of all particles. How could they claim such a thing? It's allowed because internal energy is never defined in an absolute sense, because chemical and nuclear energy would have to be included, and they are omitted. So we are talking only about a change in internal energy during a process, not the absolute amount of internal energy. If an exothermic or endothermic chemical reaction occurs, the assumption that makes the first law possible would no longer be valid.

delta U = Q-W is like saying the increase in a bank account balance equals deposits minus withdrawals. If you have a chemical reaction that releases heat, that's like earning some interest on the money, so the balance sheet no longer adds up.

4. Jan 28, 2010

### fluidistic

Thanks a lot. Very clear explanation. I'm having a good wake-up.

5. Jan 28, 2010

### mikelepore

To put it another way, the kinetic theory of gases begins by assuming that the particles will rarely interact with each other at all, and that the main thing the particles will do is travel in straight lines in between when they bounce off the container walls. In the rare cases where the particles do interact with each other, the only kind of interactions among them will be perfectly elastic collisions. Such a theory isn't intended to study a case where chemical reactions are happening.