Using E=mc^2 does thermal energy add to an object's mass?

[svenskaTom]

Hi everybody, I hope this is the appropriate place to post this question:

A middle school physics book here in Sweden poses this question after giving a brief explanation of E = mc²:

According to Einstein's formula mass and energy are two sides of the same thing. Does this mean that:
a) a new battery weighs more than a battery run out?
b) a hot iron weighs more than a cold iron?

For you Swedish speakers here is the original text:

Enligt Einsteins formel så är massa och energi två sidor av samma sak. Innebär det att
a) ett nytt batteri väger mer än ett batteri som tagit slut?
b) ett varmt strykjärn väger mer än ett kallt strykjärn?

So my answer is "Yes" to both since the additional potential (chemical) energy in the battery and the additional thermal energy of the hot iron adds to the respective masses. Forget that the additional mass is so small as to be unmeasureable, the book is talking about the implications of E = mc².

The teacher says that the answer is "No" to both, the masses are the same in both cases.

Am I wrong? lol, so much for trying to help out with homework

thanks, Tom

 

[phinds]

I think you are correct.

 

[DrClaude]

Hej Tom, välkommen till PF!

You are indeed correct.

A simplified way to see this is as follows. You probably (and hopefully so does your teacher) know that as an object accelerates, its mass gets bigger. This is the reason why nothing that has mass when at rest can ever go at the speed of light: it gets heavier as it goes faster, and would have an infinite mass at the speed of light, which would require an infinite amount of energy to achieve. In the second example in the book, you can see the increase in energy as an increase in motion. In the hot iron, the atoms are oscillating faster due to the higher temperature, and therefore have more mass.

For the battery, the analogy doesn't work so well, because quantum mechanics tells us that the electrons are not moving in the usual sense of the word, but the chemical energy in the battery is stored through the electrons and the bonds between atoms, and the total mass is greater when there is more energy.

 

[Dr Bee]

Dr Claude : perfect answer , I agree entirely .

 

[svenskaTom]

Thanks, for the answers! Now what to say to this teacher...

 

[CWatters]

Did you show her the whole question? If you ask some people if a charged battery weights more than an empty one they will answer "no because the number of electrons in the battery doesn't change, they just move".

The change in mass due to e=mc^2 is very small.

 

[svenskaTom]

The problem was assigned by the teacher as homework.

 

[svenskaTom]

Hej Tom, välkommen till PF!

You are indeed correct.

A simplified way to see this is as follows. You probably (and hopefully so does your teacher) know that as an object accelerates, its mass gets bigger. This is the reason why nothing that has mass when at rest can ever go at the speed of light: it gets heavier as it goes faster, and would have an infinite mass at the speed of light, which would require an infinite amount of energy to achieve. In the second example in the book, you can see the increase in energy as an increase in motion. In the hot iron, the atoms are oscillating faster due to the higher temperature, and therefore have more mass.

For the battery, the analogy doesn't work so well, because quantum mechanics tells us that the electrons are not moving in the usual sense of the word, but the chemical energy in the battery is stored through the electrons and the bonds between atoms, and the total mass is greater when there is more energy.

Hej DrClaude! vad bra att du talar svenska. tack för svaret!

 

[theodoros.mihos]

$E=mc^2$ comes from the invariant amount $E^2 = c^2p^2 + m^2c^4$ through relative frames.
What is the relation with questions like a), b) ?

 

[svenskaTom]

I seems that the others on this forum are more knowledgeable than I but my impression is that if E (of the system) increases then, since c is invariant, then p and/or m must go up to balance your equation.

 

[theodoros.mihos]

For 4D space-time E/c is the 4th momentum component.

 

[svenskaTom]

and...?

 

[theodoros.mihos]

See this. Energy is not like oil inside olives, is a defined amount like mass.
Relativity can not be used to answer questions like "how fast must be a bar of 10m length traveling to fit on storage 5m length".

 

[svenskaTom]

I don't know where you are going with this. The question was does E = mc² (or E²=c²p²+m²c⁴ )imply that the mass of an system increases as it gets hotter? Is your answer no to that?

 

[Doc Al]

I don't know where you are going with this.

I suspect no one does.

DrClaude gave you the answer.