# How long will it take to temperatures of two solids to become equal?

If I have two solids with commmon area where they are touching each other, is there any way for calculating the time it will take to them to become equal? For example, I have two blocks of different materials with different temperatures. They touch each other on one side. Can I calculate the time until their temperatures become equal?

EDIT: According to your answer, I found this formula:

$$\Delta Q=\frac{\lambda S(T_2-T_1)}{L}\,\Delta t$$ Can I calculate $\lambda$ for my example as proportion of weights? $$\lambda_{r} = {m_{1}\lambda_{1}\over m_{1} + m_{2}} + {m_{2}\lambda_{2}\over m_{1} + m_{2}}$$

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## 1 Answer

The heat flow between them is proportional to the temperature difference, the thermal conductivity of the junction and the area.

In theory then their temperatures will never become equal - as the temperature difference falls the heat flow decreases asymptotically. You can however easily calculate or model how long it will take for the temperature difference to drop to any arbitrary small value.

In practice the heat flow is very sensitive to the junction between them, the flatness of the surfaces, how clean they are and how much pressure pushes them together.

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Thanks. I found something on wikipedia, but I don't understand thermal conductivity of junction. Is the calculation in my question edit correct? – user35443 Oct 12 '13 at 10:00
The heat content of each object depends on the mass and specific heat capacity, not the weights – Martin Beckett Oct 12 '13 at 10:05
What should I use there then? How can I calculate conductivity of junction? – user35443 Oct 12 '13 at 10:23
If these are real parts then there are handbooks with the conductivity of junctions based on materials surface finish and pressure - or you experiment. If it is just an excercise you assume the connection is perfect - with no thermal resistance. – Martin Beckett Oct 21 '13 at 1:45