Heat needed to expand a circular metal plate

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SUMMARY

The discussion centers on calculating the thermal energy required to expand a circular metal plate when its diameter is doubled. Given that the temperature change (ΔT) is constant at 18°C and the specific heat capacity (c) remains unchanged, the mass of the plate is the determining factor. Since the volume of the plate increases fourfold with the diameter doubling, the thermal energy required for the larger plate is conclusively four times that of the original, resulting in a total energy requirement of 4Q Joules.

PREREQUISITES
  • Understanding of the formula Q = mcΔT
  • Knowledge of thermal expansion principles
  • Familiarity with concepts of mass and volume in geometric shapes
  • Basic understanding of specific heat capacity
NEXT STEPS
  • Research the principles of thermal expansion in materials
  • Learn about the specific heat capacity of different metals
  • Explore the relationship between volume and surface area in geometric shapes
  • Study the effects of temperature changes on material properties
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This discussion is beneficial for students in physics or engineering, particularly those studying thermodynamics and material science, as well as professionals involved in thermal analysis and material properties assessment.

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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Thank you very much
 

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