We know from the principle of calorimetry that if two objects of different temperature are put in thermal equilibrium, heat gets transferred from the hot object to the cold object. We also know that if the system is kept in thermal isolation and chemical reaction or other means of mass transfer are not allowed between the objects then heat given by the hot object equals heat taken by the cooler object. My question is can we find the time required for this heat transfer to happen given the masses of the objects, the temperatures of the objects, and their specific heat capacities? If not, what else do we need to know about the system and given that information how can we find the time required for the heat transfer to happen?

Faithfully, Sreejato Bhattacharya

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## Comments

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TopNewestI think the time required for the heat transfer depends upon the method of heat transfer. There are three major methods of heat transfer - Conduction, Convection and Radiation. All these processes have different formulas for time required to transfer heat until equilibrium is reached. The last but not the least, Newton law of cooling which could be used for small temperature differences is used to calculate the time required for some body like tea to cool down to room temperature. You can read about this here in detail - http://en.wikipedia.org/wiki/Convective

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I saw the Newton's Law of Cooling, but I think it works only for small heat transfer, because the term \( \frac{dQ}{dt} \) is present in the L.H.S. Conduction, convection, and radiation are three methods of heat transfer, so their formulae must be different. Can anyone please give me a formula to calculate the time required for a heat transfer to happen in general (i.e. for all the three processes)?

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I am not sure about this but if you want to find the time required for heat transfer in general, you need to integrate small heat tranfers that take place in infintesimal time through all the three processes. This is something you should leave to the computer. Although time required for heat tranfer through a single process you can calculate quite easily. For heat transfer through conduction dQ/dt = k•A•(T1 - T2)/d. You can read about this here (http://www.physicsclassroom.com/Class/thermalP/u18l1f.cfm). For conduction the rate depends on the fourth power of Temperature at which the body is currenly present (http://rpaulsingh.com/teaching/LectureHandouts/handout_radiation.pdf). So you can see the contrast among the two formulas. They are quite different.

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