# Entropy problem involving saltwater uptake into a cell

1. May 12, 2013

1. The problem statement, all variables and given/known data
For public health reasons, you are investigating small systems that turn sea water into drinking water. One portable system takes a volume of saltwater and produces two thirds that volume of freshwater with an increased concentration of salt in the other third of the volume. A typical salinity of seawater is 3.5% and its density is 1025 g/liter. To be practical, this system must run on a small solar cell array. Your first step is to calculate the minimum power necessary to produce enough drinking water for a person in an ordinary environment in a reasonable amount of time. Checking your period chart you find, hydrogen has 1 proton, oxygen has 8 protons and 8 neutrons, sodium has 11 protons and 12 neutrons, and chlorine has 17 protons and 18 neutrons.

2. Relevant equations

F = ma?

3. The attempt at a solution
I really want to work through this problem with someone on here. Entropy is the one major topic I feel clueless on and this is pretty much the only sample problem I have to practice with before my final exam this week. If someone could work through this problem with me, it'd be so greatly appreciated. I'm unsure on how to begin it...

Last edited: May 12, 2013
2. May 12, 2013

### haruspex

3. May 12, 2013

That link was a little bit too complex for this problem but thank for you it though. I think I figured it out otherwise. I have to think about the molecules being all over the place initially to then thinking about how the NaCl molecules are moved to one third the volume of the water. So it's all about the states of the NaCl molecules. I know that work reduce entropy in a system, for which the equation is W = -T x Sf-Si. And entropy is calculated by: S = k ln (changes in state). So Sinitial would consist of k ln (Vinitial / Vmolecules)^N, showing for the N number of states of NaCl molecules. Then Sfinal would be k ln (Vfinal / Vmolecules)^N, all assuming that the temperature T is constant.

Last edited: May 12, 2013
4. May 12, 2013

### haruspex

Yes, that's about as far as my vague understanding goes, but I couldn't see why you needed to know the proton and neutron counts separately. You'd only need the atomic masses for that, no? So I wondered whether you had to consider electrostatic interactions of the ions. But then you'd need to take into account that water is only partly ionised.
Wrt temperature, it has to increase, surely?

5. May 12, 2013

Yes, I believe I only need proton and neutron counts for determining mass of NaCl. However, do I also need to determine the number of molecules in the system too then? That I was unclear on. Otherwise, I know I'm also provided with the salinity and the density of the saltwater too so I'm not sure what I need to do with that. Otherwise, going off of what I've determined about the entropy, I find I come up with an answer of W = T k ln (3).

W = -T Sf-Si

= T k( ln V/3/Vo)N +k (V/Vo)N

= T k ln (V/3/Vo)N/V/Vo)N

= T k ln(3)

Not sure if there is much after that or not.

6. May 13, 2013

### haruspex

It won't be NaCl molecules, it will be Na+ and Cl- ions. From the salinity you can calculate the number of each per unit volume. OTOH, I guess there have to be an equal number of + and - ions in each subsystem, so maybe it's right to treat them as molecules.