Page 41 - FINAL DBS10012_HEAT TEMPERATURE 20102022 (2) (1)

4) If 2 kg of hot water at 100°C is added to 10 kg of cold water at 28°C and stirred well, what
is the final temperature of the mixture? (Neglect the heat absorbed by the container and

the heat lost to the surroundings.)

Solution:

Quantity Material

Hot water Cold water

Mass, m 2 10
Specific Heat Capacity, c
4200
-1
-1
(J kg °C )
Initial temperature, θ1 100°C 28°C

Final temperature, θ2 ?

Heat lost = Heat gained

-Qlost = Q gained
-mc θ = mc θ
- [2 x c x (θ2 -100°C)] = 10 x c x (θ2 – 28°C)

-2 (θ2 -100°C) = 10 (θ2 – 28°C)

200 – 2θ2 = 10θ2 -280
12θ2 = 480

θ2 = 40 °C
(Final temperature of the maximum is 40°C)

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