Equilibrium temperature and Dulong-Petit law

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SUMMARY

The discussion focuses on calculating the equilibrium temperature of a thermally insulated system consisting of 1 mole of a diatomic ideal gas at 100K and 2 moles of a solid at 200K, with the solid obeying the Dulong-Petit law. The relevant equations include the specific heat capacity derived from the Dulong-Petit law (c = 3R/M) and the heat transfer equations for the gas (Qv = 2.5 * R * ΔT and Qp = 3.5 * R * ΔT). The solution simplifies due to the absence of work done, as the system is isochoric and thermally insulated, leading to a straightforward calculation of the equilibrium temperature.

PREREQUISITES
  • Understanding of thermodynamics principles, specifically the concepts of thermal insulation and equilibrium.
  • Familiarity with the Dulong-Petit law and its application to solid materials.
  • Knowledge of ideal gas behavior and the associated equations of state.
  • Basic proficiency in heat transfer calculations and specific heat capacity.
NEXT STEPS
  • Study the Dulong-Petit law in detail to understand its implications for different materials.
  • Learn about the principles of thermally insulated systems and their behavior during thermal equilibrium.
  • Explore the derivation and application of specific heat capacities for diatomic gases.
  • Investigate isochoric processes and their significance in thermodynamics.
USEFUL FOR

Students and professionals in thermodynamics, particularly those studying heat transfer, ideal gas behavior, and material properties, will benefit from this discussion.

ChrisBaker8
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Homework Statement



A thermally insulated system consists of 1 mole of a diatomic ideal gas at 100K and 2 moles of a solid at 200K that are separated by a rigid insulating wall. Find the equilibrium temperature of the system after the insulating wall is removed, assuming the solid obeys the Dulong-Petit law. (Assume that the container is divided in such a way that there is no change in volume of the substances when the insulating wall is removed)

Homework Equations



c = 3R/M (D-P law)

Qv (gas) = 2.5 * R * \DeltaT
Qp (gas) = 3.5 * R * \DeltaT

c = C/m

c' = C/n

The Attempt at a Solution



I'm not sure how to start this without knowing what the substances are. Since there's no change in volume the changes are isochoric, therefore no work done, and the change in internal energy is equal to the heat added.
 
Last edited:
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The system is thermally insulated. How can heat be added?
 
...I didn't notice that part, that simplifies things. Thanks.
 

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