For taking bath, water at 40⁰C is required. Calculate the mass of cold water at 15⁰C which is to be added in 60 Kg water at 100⁰C for bathing purpose

Energy added to cold water, E1

E1 = m•Cp•ΔT = 6 x 4.187x(42-20) = 6x4.187x22

Energy lost by hot water, E2:

E2 = X(CpΔT) = X x 4.187 x (75-42) =X x 4.187 x 33

So, since E1 = E2

6x4.187x22 = X x 4.187 x 33

X = 6x22/33 = 4.0kg

So the mass of the hot water added to the 6kg of cold water is 4.0kg

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