200. grams of copper at 15°c are mixed with 200 grams h20 at 60°c. if the final
temperature of the mixture is 42.7oc, what was the mass of the water?

29.467 g

From the question;

Mass of copper is 200 g

Initial temperature of copper is 15°C

Mass of water is 200 grams

Initial temperature of water is 60°C

Final temperature of the mixture is 42.7 °C

We are required to calculate the mass of water

Quantity of heat, Q = Mass × specific heat capacity × change in temperature

Specific heat capacity of copper = 0.385 J/g°C

Change in temperature, ΔT = 42.7°C - 15°C

                                             = 27.7° C

Q = mcΔT

Q = 200 g × 0.385 J/g°C × 27.7°C

  = 2132.9 Joules

Specific heat capacity of water is 4.184 J/g°C

Change in temperature, ΔT = 42.7°C - 60°C

                                              = -17.3 °C

Assuming the mass of water is m

Then

Q = m × 4.184 J/g°C × 17.3 °C

   = 72.3832m joules

The heat gained by the copper metal is equal to the heat released by the water.

Therefore;

2132.9 Joules = 72.3832m Joules

m = 2132.9 J ÷  72.3832 J

   = 29.4668

   = 29.467 g

Therefore, the mass of water is 29.467 g