What Is the Equilibrium Temperature in an Adiabatically Isolated System?

[sodaboy7]

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

m_gasc_gas(T-100) = m_solidc_solid(200-T)

m_gasc_gas = Q_gas = 5/2 nRT ( 5 is degree of freedom, I guess so)

The Attempt at a Solution

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

4. Answer

171K

 

[Redbelly98]

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

m_gasc_gas(T-100) = m_solidc_solid(200-T)

m_gasc_gas = Q_gas = 5/2 nRT ( 5 is degree of freedom, I guess so)

The Attempt at a Solution

5/2 nRT = Q = m_solidc_solid(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 m_solid shouldn't be part of the calculation.

 

[sodaboy7]

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.

 

[Redbelly98]

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.