Common temperature for thermal equilibrium

[Cisneros778]

Homework Statement

One mole of copper at a uniform temp. of 0 Celsius is placed in thermal contact with a second mole of copper which, initially, is at a uniform temperature of 100 Celsius. The pressure in the system is maintained at 1 atm. The two moles of copper are thermally insulated from the surroundings. Temperature dependence of the constant pressure heat capacity of solid copper can be described by:
Cp = 33.64 + 6.28x10^-3*T J/mol*K

a) Calculate the common temperature of the 2 mole system, which is contained in an adiabatic enclosure, when thermal equilibrium is attained.

2. Homework Equations

dH = cp*dt
dS = dq/T

The Attempt at a Solution

Since it is in an adiabatic enclosure, dq = 0.
ΔH= H2 - H1 = dq = 0

but in the solution, it says ΔH = H1 + H2 = 0
∫₂₇₃^Tfcp*dT = - ∫₃₇₃^Tfcp*dT

I don't understand why this approach is correct.

 

[Chestermiller]

Homework Statement

One mole of copper at a uniform temp. of 0 Celsius is placed in thermal contact with a second mole of copper which, initially, is at a uniform temperature of 100 Celsius. The pressure in the system is maintained at 1 atm. The two moles of copper are thermally insulated from the surroundings. Temperature dependence of the constant pressure heat capacity of solid copper can be described by:
Cp = 33.64 + 6.28x10^-3*T J/mol*K

a) Calculate the common temperature of the 2 mole system, which is contained in an adiabatic enclosure, when thermal equilibrium is attained.

2. Homework Equations

dH = cp*dt
dS = dq/T

The Attempt at a Solution

Since it is in an adiabatic enclosure, dq = 0.
ΔH= H2 - H1 = dq = 0

but in the solution, it says ΔH = H1 + H2 = 0
∫₂₇₃^Tfcp*dT = - ∫₃₇₃^Tfcp*dT

I don't understand why this approach is correct.

For the combined system of two moles,
ΔH=∫₂₇₃^Tfcp*dT +∫₃₇₃^Tfcp*dT=0

where the first term represents the change in enthalpy of the mole initially at 0 C, and the second term represents the change in enthalpy of the mole initially at 100 C.