Heat needed to expand a circular metal plate

In summary, the problem states that a circular metal plate of diameter D requires Q Joule of heat to expand when the temperature changes from 40oC to 58oC. The question asks for the thermal energy needed to expand an identical metal plate with twice the diameter for the same increase in temperature. Using the equation Q = mcΔT, we can assume that the mass and specific heat (c) remain constant. Since the diameter is doubled, the area becomes 4 times and the volume becomes 4 times as well. Assuming density is constant, the answer is 4Q.
  • #1
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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  • #2
songoku said:
Should I assume
Yes, that's all you are given.
 
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Likes songoku
  • #3
Thank you very much
 

1. How does heat affect the expansion of a circular metal plate?

Heat causes the molecules in a metal plate to vibrate more rapidly, which in turn causes them to take up more space and expand.

2. How much heat is needed to expand a circular metal plate?

The amount of heat needed to expand a circular metal plate depends on the type of metal, its dimensions, and the desired amount of expansion. It can be calculated using the coefficient of thermal expansion for the specific metal and the change in temperature.

3. Can a circular metal plate expand without the addition of heat?

Yes, a circular metal plate can expand without the addition of heat. This is known as thermal expansion and occurs when the temperature of the metal increases due to its surroundings.

4. What happens when a circular metal plate expands due to heat?

When a circular metal plate expands due to heat, it increases in size and its dimensions change. This can cause the plate to warp or bend, depending on its shape and the amount of expansion.

5. Is the expansion of a circular metal plate reversible?

Yes, the expansion of a circular metal plate is reversible. When the temperature decreases, the metal plate will contract and return to its original size and shape. However, repeated cycles of expansion and contraction can cause fatigue and damage to the metal.

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