Question

A 4 g good block at 250 °C and a 1 g aluminum block at 120 °C are placed on a 45 g sheet of copper at 20 °C. If the three objects are well-insulted from their surroundings, what equilibrium temperature do they eventually reach? The heat capacities of good, aluminum are 129, 900 and 385 J/(kgK), respectively.

Answer 1

Suppose the final temperature is T.
Now Using energy conservation:
Heat gained by water and calorimeter = Heat released by copper
Q1 + Q2 = Q3
m1*C1*dT1 + m2*C2*dT2 = m3*C3*dT3
dT1 = Tf - Ti = T - 120
dT2 = T - 20
dT3 = 250 - T
m1 = mass of aluminium = 0.001 kg
m2 = mass of copper = 0.045 kg
m3 = mass of aluminium = 0.004 kg
Now using given values:
0.001*900*(T - 120) + 0.045*385*(T - 20) = 0.004*129*(250 - T)
Now Solving above equation
T = (0.001*900*120 + 0.045*385*20 + 0.004*129*250)/(0.001*900+ 0.045*385 + 0.004*250)
T = 30.35 C
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