Calculating Linear Expansion with Specific Heat Capacity and Mass Density?

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SUMMARY

The discussion centers on calculating linear expansion using specific heat capacity and mass density. A specific heat capacity of 390 J/(kg K) is confirmed as necessary for accurate calculations. The importance of incorporating mass density into the solution is emphasized, as it directly influences the linear expansion outcome. Participants seek clarification on the correct interpretation of the heat capacity value to ensure precise results.

PREREQUISITES
  • Understanding of specific heat capacity, particularly in units of J/(kg K)
  • Familiarity with mass density concepts and calculations
  • Basic knowledge of linear expansion principles in physics
  • Ability to apply thermodynamic equations in problem-solving
NEXT STEPS
  • Research the relationship between specific heat capacity and linear expansion
  • Study the impact of mass density on thermal expansion calculations
  • Explore thermodynamic equations relevant to heat transfer and expansion
  • Practice problems involving specific heat capacity and mass density to solidify understanding
USEFUL FOR

Students and professionals in physics, engineering, and materials science who are involved in thermal analysis and expansion calculations will benefit from this discussion.

Kara4566
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Homework Statement
A 1.0m long rod of metal has a diameter of 0.75cm. This metal has
a coefficient of linear expansion α = 4.8 × 10−5 1/K, a density of 9.7 ×10^3 kg/m^3, and heat capacity of 390 J/K.
How much energy needs to be added as heat to increase the length of the rod by 7.5 × 10−3m?
Relevant Equations
change in Length= (Initial Length)(Coefficient of linear expansion)(change in temperature)
242182


Above is my attempt at a solution, however, this did not yield the correct answer. Any help is greatly appreciated!
 
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I wonder if the heat capacity of 390 J/K is really meant to be a specific heat capacity of 390 J/(kg K). Then, you can make use of the mass density given in the problem.
 
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