what is the difference in energy

Question

A 100 g sample of a hypothetical metal alloy (specific heat capacity = 0.406 J/g•°C) is cooled in an ice bath (assume the metal reaches the freezing point of water). It is dried and placed in a calorimeter containing an unknown mass of water that was initially at a temperature of 20.0 °C. Assuming a lossless transfer of heat and an equilibrium temperature of 12.0 °C, what is the difference in energy (in J) of the water in the calorimeter at equilibrium?

Answer 1

Cutting to the chase, the question is asking about the difference in the temperature of the WATER in the calorimeter. Boiling this down even further, this is essentially asking "how much energy did the metal alloy gain once it was placed in the water and its temperature rose from 0º to 12.0ºC. This is based on the simple principle that

HEAT GAINED BY METAL MUST EQUAL HEAT LOST BY WATER.

heat lost by metal q== mC∆T

q = ?

m = mass = 100 g

C = specific heat = 0.406 J/gº

∆T = change in temp = 12.0 - 0º = 12º (0º being the normal freezing point of water = initial temp. of metal)

q = (100 g)(0.406 J/gº)(12º)

q = 487.2 J = heat gained by metal = heat lost by water

So, the difference in energy of the water is -487 J

(note that 100 g has only 1 sig. fig. but I've chosen to report the answer to 3 sig.figs.)