Question

1.00 kg of ice at -38.0 degrees C is dropped into 25.0 kg of water at 34.0 degrees C. What is the final temperature of the mixture?

Answer 1

As we know heat flows from a hot to a cold body. So here,the heat gained by the ice will be equal to the heat lost by the water. the heat gained by ice is partly the rise in temperature from -38 to 0 degree and melting into water at 0 degree and then rising of this 1kg water to a final temperature. This heat is lost by the 25 kg water in cooling down from 34 degrees to the final temperature. So to calculate the final temperature (say x) we equate the heat gained to heat lost

Heat energy = mass x specific heat x change in temperature

Heat gained by ice= Heat lost by water

Sp. heat of ice = 2.1 J/kg, Sp latent heat of ice = 336 J/kg, Sp. heat of water = 4.2 J/kg

1*(0-(-38))* 2.1 + 1*336 + 1* 4.2* (x-0) = 25*4.2*(34-x)

Solving for x, we get x = 28.88 degrees C