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There is no specific ratio. That would depend on many things....compound, phase and suchlike.

However there are many, many relationships that can be used to bring the two together.

A classic example would be the ideal gas equation:

PV = nRT. If everything but V and T were kept constant, you would have to say that a rise in V would mean a rise in T and vice versa. This is generally pretty accurate.

Think of a hot air balloon. You add heat to the balloon, the air heats up ( the temperature rises) and the volume of the balloon rises (it expands). So that is generally the relationship between the two...however there is no specific numerical ratio between them.

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