Identical conditions but
The figure below shows two identical, metallic spheres A and B. Both the spheres are conductive in nature and thermally insulated from outside surroundings. Initially, both are at the same temperature T. Now, both are supplied with an equal amount of heat Q (the heat is supplied into their body and hence is not obstructed by the thermal insulation).
If their temperatures after supplying the heat are T(A) and T(B), then
Note:
The string is non-conductive in nature.
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1 solution
The balls being metallic/conductive expand in size. The COM of ball B lowers causing a decreasing potential energy (note that the ball is expanding freely and not against any opposing force as the connecting point is stationary on the string) hence the lowering of COM does not affects its temperature. But, in ball A the expansion causes the ball to lift itself up, lifting the COM from the ground, which takes place at the expense of the energy possessed in the vibration of the molecules (which damp their own vibrations pushing the ball up). So, the temperature in ball A lowers than it should be.