Question

How many kilogram of hot water at 48°C must you mix with cold water at 12°C so that the temperature of the bath is 36°C? The total mass of water (hot plus cold) is 90kg

Answer 1

Given:

Temperature of hot water, T1 = 48°C

Temperature of cold water, T2 = 12°C

Final temperature = 36 °C

Total mass of water = 90 kg

Let's find the mass of hot water.

Let x represent the mass of hot water.

We have:

Mass of hot water = x

Mass of cold water = 90 - x

• Fall in temperature of hot water, ΔT1 = T1 - T = 48°C - 36 °C = 12°C

• Temperature increase of cold water, ΔT2 = 36 °C - 12°C = 24°C.

Apply the principle of calorimetry:

Heat gained by cold water = Heat lost by water

Thus, we have:

`m_1C\Delta T_1=m_2C\Delta T_2`

Where:

m1 is the mass of hot water

m2 is the mass of cold water.

Thus, we have:

`\begin{gathered} m_1\Delta T_1=m_2\Delta T_2 \\ \\ x(12)=(90-x)(24) \\ \\ 12x=90(24)-24x \\ \\ 12x+24x=2160 \\ \\ 36x=2160 \\ \\ x=(2160)/(36) \\ \\ x=60 \end{gathered}`

Therefore, the mass of hot water you must mix is 60 kilograms.

ANSWER:

60 kg