Question

A student mixes 93.7 g of water at 71.3 C with 43.7 g of water at 18.3 C in an insulated flask. What is the final temperature of the combined water?

Answer 1

The heat lost by water at 71.3^oC = heat gained by water at 18.3 ^oC

                                mcdt = m'cdt'

                                           mdt = m'dt'

Where

m = mass of water at 71.3^oC = 93.7 g

c = specific heat capacity of water

dt = change in temperature of water at 71.3^oC = (71.3-t )^oC     

                                where t is the common temperature attained by the system

m' = mass of water at 18.3^oC = 43.7 g

dt' = change in temperature of water at 18.3^oC = ( t-18.3 )^oC     

                                where t is the common temperature attained by the system

Plug the values we get

93.7x(71.3-t ) = 43.7x(t - 18.3)

2.14x(71.3-t ) = (t - 18.3)

152.8 - 2.14t = t- 18.3

           3.14 t = 171.2

                  t = 54.5 ^oC

Therefore the final temperature attained by the system is 54.5 ^oC