One mole of pure Nickel at 0°C is placed in contact with one mole of pure Nickel

Question

One mole of pure Nickel at 0°C is placed in contact with one mole of pure Nickel at 100°C. This contact occurs inside a highly insulated calorimeter chamber. The system is then allowed to come to thermal equilibrium under constant pressure conditions. The insulation of the chamber walls is usually nearly perfect, but there is a crack in the insulation of the chamber, which allows an unknown amount of heat to escape during the equilibration process. If the final measured temperature of the system at equilibrium is 47.27°C, how much heat was lost through the crack?

Explanation / Answer

General law:

Q = m*Cp*dT

CpNickel= 0.44 kJ/ kg K

Molar mass of Nickel = 58.69 kg/mol

1 mol of Nickel = 58.69 g

Let's call "1" the one mole of pure nickel at 0°C

T1= 0°C = 273 K

Tf = x (final T)

And let's call "2" the one mole of pure nickel at 100°C

T2 = 100 °C = 373 K

Tf = x

Now, theoretically:

Qreleased = - Qabsorbed

m1 Cp dT1 = - m2 Cp dT2  

m1 Cp (Tf - T1) = - m2 Cp (Tf - T2) In this scenario we don't know the final temperature (Tf), so we find it:

Tf = 323 K = 50 °C

So, Q should be: Q = m1 Cp (Tf - T1) = 1.29 kJ

But, instead, the final temperature is 47.27 °C = 320.47 K, so real Q is:

Q = m1 Cp (Tf - T1) = 1.23 kJ

The heat that was lost is

Qlost = 1.29 kJ - 1.23 kJ = 0.6 kJ

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