What Is the Equilibrium Temperature in an Adiabatically Isolated System?

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Homework Help Overview

The problem involves an adiabatically isolated system containing 1 mol of a diatomic gas at 100K and 2 mol of a solid at 200K, separated by a rigid adiabatic wall. The goal is to find the equilibrium temperature after the wall is removed, with the solid following the Dulong-Petit law.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the energy balance between the gas and the solid, referencing equations related to heat transfer and specific heat capacities. There are questions about the application of the Dulong-Petit law and the role of mass in the calculations.

Discussion Status

Some participants have provided calculations leading to a proposed equilibrium temperature, while others express uncertainty about the methods used and the assumptions made, particularly regarding the Dulong-Petit law and the mass of the solid.

Contextual Notes

There is mention of a reference answer in the textbook, but participants have not yet reached a consensus on the reasoning or calculations leading to that answer. The discussion reflects varying levels of understanding regarding the principles involved.

sodaboy7
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Homework Statement


An adiabatically isolated system consists of 1 mol of a diatomic gas 100K and 2 mol of a solid at 200K separated by a rigid adiabatic wall. Find the equilibrium temperature of system after adiabatic wall is removed, assuming that the solid obeys the Dulong-Petit law.


Homework Equations


mgascgas(T-100) = msolidcsolid(200-T)

mgascgas = Qgas = 5/2 nRT ( 5 is degree of freedom, I guess so)

The Attempt at a Solution



5/2 nRT = Q = msolidcsolid(200-T)

4. Answer

171K
 
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sodaboy7 said:

Homework Statement


An adiabatically isolated system consists of 1 mol of a diatomic gas 100K and 2 mol of a solid at 200K separated by a rigid adiabatic wall. Find the equilibrium temperature of system after adiabatic wall is removed, assuming that the solid obeys the Dulong-Petit law.


Homework Equations


mgascgas(T-100) = msolidcsolid(200-T)

mgascgas = Qgas = 5/2 nRT ( 5 is degree of freedom, I guess so)

The Attempt at a Solution



5/2 nRT = Q = msolidcsolid(200-T)

4. Answer

171K
I agree with that answer, though you didn't really show how you got it. You haven't shown how you used the Dulong-Petit law, and msolid shouldn't be part of the calculation.
 
The answer was given on back pages of the book. I have not got any answer yet. I don't know how they got that answer.
 
What does your book or class notes say about the Dulong-Petit law? You should look that up, it relates the energy of the solid and its temperature change.
 

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