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Different molecules have different specific heats, such as water, which has a very high specific heat due to strength of inter-molecular attractions.

If temperature is the random kinetic energy of individual molecules/ atoms, and for different substances with varying specific heats, it takes a different amount of energy (heat) to cause the same amount of change in kinetic energy of molecules/atoms, does that mean that temperature is relative (e.g. 77 degree water molecules do not contain the same amount of kinetic energy as 77 degree copper atoms)?

If kinetic energy is not equivalent, then what causes both substances in the system to not have an additional net/loss of kinetic energy if both substances are at the same temperature (assuming no energy lost to the surroundings)?

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As well as the kinetic energy that molecules have due to their translational motion they also can have kinetic energy associated with rotational and vibrational modes.

When it comes to temperature only the translational kinetic energy is considered and if two bodies have the same temperature the average translational kinetic energy of the molecules which make up the two bodies is the same.

However, there can be a difference between the average total kinetic energy of water molecules and copper molecules at the same temperature due to the fact that their molecules might have differing amounts of rotational and vibrational kinetic energy but the average translational kinetic energy of the molecules will be the same.

When specific heat is considered then all forms of kinetic energy and potential energy that the molecules possess come into play.
This also introduces the possibility that some of the heat supplied to a body is used to do work because the body expands against its surroundings.

This is a factor which is small and tends to be ignored for solids and liquids which do not expands by very much when their temperature changes but must be included when considering the specific heat capacity of gases.

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