Heat needed to expand a circular metal plate

AI Thread Summary
To calculate the thermal energy needed to expand a circular metal plate with twice the diameter, one must consider that the mass increases with the volume of the plate. Given that the diameter is doubled, the area increases by a factor of four, leading to a fourfold increase in volume and mass, assuming constant height and density. The specific heat capacity and temperature change remain constant, so the thermal energy required for the larger plate is four times that of the original plate. Therefore, if the original plate requires Q Joules, the larger plate will need 4Q Joules for the same temperature increase. The conclusion is that the thermal energy needed is indeed 4Q.
songoku
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Homework Statement


A circular metal plate of diameter D needs Q Joule of heat to expand and the temperature changes from 40oC to 58oC. What is the thermal energy needed to expand identical metal plate having twice the diameter for same increase in temperature?

Homework Equations


Q = mcΔT

The Attempt at a Solution


ΔT and c will be constant, but I am not sure about the mass. Should I assume the shape of the circular metal plate is cylinder and the height is constant during heating? So twice diameter means the area becomes 4 times and volume becomes 4 times? Then assuming density is constant, the answer is 4Q?

Thanks
 
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songoku said:
Should I assume
Yes, that's all you are given.
 
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