Page 39 - FINAL DBS10012_HEAT TEMPERATURE 20102022 (2) (1)

2) A piece of metal of mass 0.5 kg is heated to 100 °C in boiling water. It is then transferred
into a well-insulated beaker containing 1.5 kg of water at 27 °C. If the final steady

temperature of the water in the beaker is 32 °C, what is the specific heat capacity of the
metal? Assume that there is no loss of heat to the surroundings and ignore the heat

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transferred to the beaker. (Specific heat capacity of water is 4200 J kg °C )
Solution:

Quantity Material

Metal Water
Mass, m 0.5 1.5

Specific Heat Capacity, c ? 4200
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-1
(J kg °C )
Initial temperature, θ1 100°C 27°C
Final temperature, θ2 32°C

Q gained = - Q lost
(mc ∆q ) water = - (mc ∆q ) metal
1.5(4200) (32 °C- 27°C) = - [0.5(c)(32°C-100°C)]

31 500 J = 34 c J

c = 31500
34
-1
c = 926.5 J kg °C -1

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