# Heat transfer between 3 bodies

#### Euler123

Hi i have problem i want to solve that is related to an industry. The problem is that i have 3 rectangular wood plates. The middle plate starts with 120c degrees. The upper and lower plate are being constantly cooled so they keep a temperature of 20 degrees celsius all the time.
The question i want to know is how is the mass of body 2 affected in regards to the cooling of the system(m1 and m3)?

What impact does the heat transfer have on the middle plate (m2)?

My thermodynamical skills lack a bit, i tried to start to approach the problem in a most simple matter. I assume the principal is the same, so later i can put up a differential heat equation if needed.

#### HallsofIvy

The mass of body 2? Mass is not influenced by temperature at all. If you are asking about the change in temperature of body 2, then dT/dt= -k1(T- 20)- k2(T- 20)= (k1+k2)(T- 20). k1 and k2 depend upon the properties of the materials.

#### oz93666

The mass of body 2? Mass is not influenced by temperature at all.
To be precise increasing the temperature of an object does increase its mass...

Energy is equivalent to mass .... so if we have a 1 kilo mass (at sea level) and take it up mount everest we have increased it's mass ...mgh gives a number in Joules , convert this to mass (by E=mc2) to find the increase in kilograms...

If we throw our mass through the air at velocity v , we have increased it's mass 1/2mv2 , converted to kilos ...

And if we heat it , we have added energy , convert to mass by E=mc2
In a heated object the molecules are moving more quickly , increased speed increases mass of molecules ....

In practice the increase is so small it's negligible...

To answer the question from Euler ... the only way mass will change is by movement of moisture in the wood ... even "dry " wood has 5% moisture , by heating the middle plate to 120C you will drive the moisture out to the cooler plates , this process transfers heat and mass.