Question

A 35 g block of ice is cooled to −83 ◦C. It is added to 565 g of water in an 87 g copper calorimeter at a temperature of 22◦C. Find the final temperature. The specific heat of copper is 387 J/kg · ◦C and of ice is 2090 J/kg · ◦C . The latent heat of fusion of water is 3.33 × 105 J/kg and its specific heat is 4186 J/kg · ◦C . Answer in units of ◦C.

Answer 1

Step-by-step explanation:

Heat gained by ice in warming up to 0⁰C = .035 x 2090 x (83-0)= 6071.45 J

heat used up by ice to melt at 0⁰C = .035 x 3.33 x 10⁵ J = 11655 J

Heat used up in warming up water to t⁰C = .035 x 4186 x t = 146.51 t

heat released by warm water to cool from 22⁰C to t = .565 x 4186 x ( 22 - t )

=52032 -2365.1 t

heat released by copper calorimeter to cool from 22⁰C to t = .087 x 387 x ( 22 - t ) = 740.72 - 33.7 t

total heat released = 52032 -2365.1 t + 740.72 - 33.7 t

= 52772.72 - 2398.8 t

Heat lost = heat gained

52772.72 J- 2398.8 t = 6071.45 J + 11655 J + 146.51 t

2545.31 t = 35046.27

t = 13.8°C.