# Homework Help: Mass energy equivalence

1. Mar 21, 2016

### erisedk

1. The problem statement, all variables and given/known data
If mass-energy equivalence is taken into account, when water is cooled to form ice, the mass of water should increase, decrease or remain unchanged?

2. Relevant equations
E = mc2

3. The attempt at a solution
Since the internal energy of ice is less than water, it's mass should also be less. This might be a completely wrong interpretation though because the answer says increase. I haven't really studied mass energy equivalence in much detail, I just know the basics from nuclear physics.

2. Mar 21, 2016

### IAN 25

In any process where the internal energy decreases, energy must be liberated and pass to the surroundings - right? So, this energy has a mass equivalent given by E = mc2 . So, the mas must ...

3. Mar 21, 2016

### erisedk

Decrease? Because energy of the body decreased and went into the surroundings? Like in nuclear physics, the rest mass of the nucleus is lower than the mass of the individual nucleons because some of the mass gets converted into binding energy. So here since some of the energy has gone away, the mass should be lower, I guess.

4. Mar 21, 2016

### Buzz Bloom

Hi erisedk:

I think you are correct. The ice would have a lower combined mass-energy than the water. Can you post some context from where the answer that says "increase" comes from?

Regards,
Buzz

5. Mar 21, 2016

### erisedk

It was on an old practice test. That's okay though, the answers can be wrong sometimes. I think I'm correct too.

6. Mar 21, 2016

### erisedk

Thanks :)

7. Mar 21, 2016

### RedDelicious

I think it is no change. E = mc^2 or m = E/c^2 where m is the rest mass. The rest mass is the mass measured by an observer in a reference frame where the object is at rest, and because phase changes don't affect mass, the rest mass should be constant. You'll measure the same mass as liquid and as ice. To account for the change in energy, perhaps the structural change balances the energy lost during the phase change.

Last edited: Mar 21, 2016
8. Mar 21, 2016

### Buzz Bloom

Hi Red:

I am pretty sure you are mistaken. Think of what happens if you put an ice cube a 0 deg C into water at say 10 deg C. The ice melts and the water gets colder. The energy lost by the water melts the ice. Although it is not possible for thermodynamic reasons, if you ran the scenario backwards, some water would warm as the some other water freezes.

Regards,
Buzz

9. Mar 22, 2016

### IAN 25

All forms of energy have an equivalent value of rest mass whether or not it is actually realised as 'mass'. The rest mass in an inertial frame is the same for all intertial observers yes but that does not mean it cannot be converted into energy within a given frame - by nuclear fission for example.

erisedk your conclusion is correct, the mass will be lower. One has to realise here that the amounts of mass equivalence are extremely small, E/c2 small!

10. Mar 22, 2016

### Buzz Bloom

Hi IAN:

I have learned over the past year from my participation in the PF that "mass" always means rest mass, except when some alternative and not generally current usage is specifically explained as to be what is meant. The term, "relativistic mass" is also generally no longer used for what seems to me to be a rather obscure subtle reason. I am not quite sure what is the preferred phraseology to replace "relativistic mass", but I think "mass-energy" is acceptable to mean the total mass equivalent of the sum of rest mass and kinetic (and possibly other forms of) energy.

Regards,
Buzz

11. Mar 22, 2016

### IAN 25

Hi Buzz, I prefer to use 'rest mass' as it is unmistakable in its meaning. E2 - p2c2 = m2c4 being lorentz invariant.

Cheers,
Ian.

12. Jan 17, 2018

### Vaibhav shekhar

Here thermal energy decreases, therefore mass of water will increase.