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.

 

[asteriatic]

. This can be found by setting the two equations equal to each other and solving for T. The final equilibrium temperature of the system will be 171K. This is because when the adiabatic wall is removed, the system will reach thermal equilibrium and the total energy of the system will be conserved. The Dulong-Petit law states that the heat capacity of a solid is directly proportional to its temperature, so as the temperature of the solid decreases, the temperature of the gas will increase until they reach equilibrium at 171K.