Question

Lead pellets of total mass 0.76 kg are heated to 100 ∘C and then placed in a well-insulated aluminum cup of mass 0.24 kg that contains 0.42 kg of water initially at 14.3 ∘C .

What is the equilibrium temperature of the mixture?

Answer 1

Solution: From the question we have:

=>Lead pellets of total mass 0.76 kg are heated to 100 ∘C and then placed in a well-insulated aluminum cup of mass 0.24 kg that contains 0.42 kg of water initially at 14.3 ∘C

To find out: What is the equilibrium temperature of the mixture?

Lead : m1 = 0.76 kg ; T1 = 100 °C ; cp1 = 129 J/kg/K
Alu : m2 = 0.24 kg ; T2 = 14.3 °C ; cp2 = 31,75104/0,02698 = 1177 J/kg/K
water : m'2 = 0.42 kg ; cp'2 = 4186 J/kg/k
▬▬▬

m1.cp1.T1 + (m2.cp2 + m'2.cp'2)T2 = (m1.cp1 + m2.cp2 + m'2.cp'2)T3
→ T3 = [m1.cp1.T1 + (m2.cp2 + m'2.cp'2)T2 ]/(m1.cp1 + m2.cp2 + m'2.cp'2)
→ T3 = (0.76*129*100 +(0,24*1177 + 0.42*4186)*14.3)/ (0.76*129 + 0,24*1177 + 0.42*4186)
→ T3 = 13.6902 ≈ 13.7 °C