Specific heat capacity varies with temperature.

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SUMMARY

The discussion centers on calculating the average specific heat capacity of a 0.8 kg iron disk as it is heated from 20°C to 400°C, where specific heat capacity varies from 456 J/(kg·°C) at 20°C to 615 J/(kg·°C) at 400°C. The equation E = mC(dT) is utilized, and the participant suggests using calculus to find the average specific heat capacity. The proposed method includes integrating the differential form dE = m (CdT + TdC) to derive the solution.

PREREQUISITES
  • Understanding of specific heat capacity and its temperature dependence
  • Familiarity with the equation E = mC(dT)
  • Basic calculus concepts, particularly differentiation and integration
  • Knowledge of plotting functions and interpreting graphs
NEXT STEPS
  • Learn about integrating variable specific heat capacities in thermodynamics
  • Study the application of the product rule in calculus
  • Explore the concept of average values in physics
  • Investigate the relationship between temperature and specific heat capacity for different materials
USEFUL FOR

Students studying thermodynamics, physics educators, and anyone interested in the mathematical modeling of heat transfer processes.

necromanzer52
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Homework Statement


Heating a .8 kg disk of iron from 20 C to 400 C, but the specific heat capacity changes from 456 at 20 C, to 615 at 400 C. It hints that I'm supposed to find the average to solve the equation.


Homework Equations


E = mC(dT)


The Attempt at a Solution


I have a strong feeling, that I'm supposed to use calculus to solve this, but I can't think of any equations to differentiate, or how it would be, in any way, useful.

I've also thought about plotting the specific heat capacity against kelvin, and using the specific heat capacity at the midpoint (483.15k)
 
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Just a hint

dE = m d(CT)
dE = m (CdT + TdC) (product rule)

Integrate both sides and find the answer.
 

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