Does increasing the temperature of an object increase it's mass?

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SUMMARY

The discussion centers on the relationship between temperature, energy, and mass as described by Einstein's equation E=mc². It is established that heating an object, such as a rock or metal, increases its energy and consequently its mass due to the kinetic energy of vibrating atoms. The equation E=mc² applies to objects at rest, while moving objects require the equation E²=m²c⁴+p²c². Additionally, a compressed steel spring is heavier than its non-compressed state due to stored energy.

PREREQUISITES
  • Understanding of Einstein's equation E=mc²
  • Basic knowledge of kinetic energy and thermodynamics
  • Familiarity with the concepts of mass-energy equivalence
  • Knowledge of the relationship between temperature and energy
NEXT STEPS
  • Research the implications of E=mc² in different physical states
  • Study the equation E²=m²c⁴+p²c² for moving objects
  • Explore the effects of temperature on atomic motion and mass
  • Investigate the measurement of energy in compressed materials
USEFUL FOR

Physicists, engineering students, and anyone interested in the principles of thermodynamics and mass-energy equivalence will benefit from this discussion.

mcafej
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Ok, so I was just thinking about einsteins famous equation E=mc^2, and I was just wondering, if I were to take, say a rock or piece of metal. If I were to weigh it, and get it's mass, I could compute how much energy it contains. However, if I were to add heat to the rock or piece of metal by putting it into a fire to just heat it up, wouldn't the amount of energy that the rock or metal contains be higher, and so wouldn't the mass be higher (since the speed of light is constant, the only thing that can increase when the energy increases is mass, right?)? Anyways, maybe I'm missing an obvious point, but I was just curious about this, so any clarification would be great.
 
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You are absolutely correct. The measured mass would increase if you heat an object up.
 
Just remember that the equation E=mc^2 only applies to objects at rest. Objects in motion use the equation E^2=m^2c^4+p^2c^2.
 
mcafej said:
Ok, so I was just thinking about einsteins famous equation E=mc^2, and I was just wondering, if I were to take, say a rock or piece of metal. [..] if I were to add heat to the rock or piece of metal [..], wouldn't the amount of energy that the rock or metal contains be higher, and so wouldn't the mass be higher [..]? [..] any clarification would be great.

Yes that is correct; the kinetic energy of the vibrating atoms in that object adds to its mass. (I don't know if it has ever been possible to measure this effect.)

See also the conclusion of the related famous paper:
http://www.fourmilab.ch/etexts/einstein/E_mc2/www/

and a discussion of temperature:
https://en.wikipedia.org/wiki/Thermodynamic_temperature
 
Does this also mean that a steel spring would be measured heavier in a compressed state than in a non-compressed state as it has stored energy?
 
JustinRyan said:
Does this also mean that a steel spring would be measured heavier in a compressed state than in a non-compressed state as it has stored energy?

Yep!
 

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