Equilibrium temperature and Dulong-Petit law

AI Thread Summary
To find the equilibrium temperature of a thermally insulated system containing 1 mole of diatomic ideal gas at 100K and 2 moles of solid at 200K, the Dulong-Petit law is applied, which states that the molar heat capacity of the solid is related to its atomic mass. The process is isochoric, meaning no work is done, and the change in internal energy equals the heat exchanged. The initial confusion about heat addition is clarified by recognizing that the system is insulated, allowing for heat transfer between the gas and solid until thermal equilibrium is reached. The calculations involve using the specific heat capacities of both substances to determine the final equilibrium temperature. Ultimately, the equilibrium temperature can be calculated without needing to know the specific identities of the substances involved.
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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.
 
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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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