Question

Calculate the initial temperature, in °C, for a 105-g sample of aluminum (s = 0.900 J/g. K) that is added to a calorimeter (C = 107 J/K) filled with 96.5 g of water (s = 4.184 J/g. K) at 23.3 °C. The equilibrium temperature for the experiment is 35.2 °C.

Answer 1

Heat gained by water (H1) = mass of water * Specific heat capacity of water * temperature change = 96.5 g * 4.184 J/ g ⁰C * ( 35.2 - 23.3) ⁰C = 4805 Joules

Heat gained by calorimeter (H2) = 107 J / ⁰C * ( 35.2 - 23.3) ⁰C = 1273.3 Joules

Total heat gained = 4805 + 1273.3 Joules = 6078.3 Joules

Heat lost by aluminium (H3) = 105 g * 0.900 J / g ⁰ C * ( X-35.2) ⁰C = 94.5 * (X- 32.5) Joules

where X is the initial temperature of aluminium

AT equilibrium, Heat gained = Heat lost

6078.3 = 94.5* (X-32.5)

X = 96.8

Initial temperature of aluminium is 96.8 0C