I was thinking about analogies between the fields of electric force, pressure force in liquids and heat flow and am wondering whether the heat flow is grad T or grad Q.
Ive come to the conclusion that it must be grad T for the following reason:
Consider two objects of the same mass and form, at the same temperature, but with one object having a higher thermal capacity than the other, so both have the same temperature, but one has more thermal energy than the other.
If I put the two objects into contact there will be no change in temperature, so no flow of heat.
If I put the two objects together when they have different temperatures there will be heat flow.
By this reasoning I come to the conclusion that heat flow = grad T.
Im interested in any comments because I fuck up physics alot.