Question

40 g of hot water is poured in 100 g of cold water, when the temperature of cold water rises by 10°C. If the temperature of hot water is 60°C, calculate the initial temperature of cold water.

Answer 1

Substance	Mass	S.H.C.	Initial Temp.	Final Temp. = x
Hot water	40 g	4.2 Jg−1°C−1	60°C	θF = (60 − x)
Cold water	100 g	4.2 Jg−1°C−1	?	θR = 10°C

Heat given out by hot water = mcθ_F = 40 × 4.2 × (60 − x)

Heat absorbed by cold water = mcθ_R = 100 × 4.2 × 10

∴ Heat given out by hot water = Heat absorbed by cold water.

⇒ 40 × 4.2 × (60 − x) = 100 × 4.2 × 10

⇒ 2400 − 40x = 1000

⇒ 40x = 2400 − 1000

\[\Rightarrow x=\frac{1400}{40}\]

∴ x = 35°C

Thus, the temperature of the mixture = 35°C

Initial temperature of cold water = (35 − 10)°C = 25°C