Question

1- An aluminium object with a mass of 3.10 kg and at a temperature of 21.3 °C comes to thermal contact with a 7.21 kg copper object which is initially at a temperature of 86.5 °C. What is going to be the equilibrum temperature of the two objects? Neglect heat transfer between the objects and the environment. The specific heats are: cAl = 900 J/kg°C and cCu = 387 J/kg°C.

2- Three different liquids are mixed together in a calorimeter. The masses of the three liquids are:
m₁ = 385.0 g,
m₂ = 615.0 g,
m₃ = 715.0 g.
The specific heats are:
c₁ = 275 J/kg°C,
c₂ = 500 J/kg°C,
c₃ = 860 J/kg°C.
The initial temperatures of the liquids are:
T₁ = 23.0 °C,
T₂ = 57.0 °C,
T₃ = 89.0 °C.
What is going to be the final temperature of the mixture?

Answer 1

1.

Suppose the final temperature is T.

Now Using energy conservation:

Heat gained by aluminum = Heat released by copper

Q1 = Q2

m1*C1*dT1 = m2*C2*dT2

dT1 = Tf - Ti = T - 21.3

dT2 = 86.5 - T

m1 = mass of aluminum = 3.10 kg

m2 = mass of copper = 7.21 kg

Now using given values:

3.10*900*(T - 21.3) = 7.21*387*(86.5 - T)

Now Solving above equation

T = (3.10*900*21.3 + 7.21*387*86.5)/(3.10*900 + 7.21*387)

T = 53.90 C = final equilibrium temperature

Please ask 2nd question as a new question