Asheet of gold weighing 13.6 g and at a temperature of 16.7°c is placed flat on a sheet of iron weighing 24.5 g and at a temperature of 46.4°c. what is the final temperature of the combined metals? assume that no heat is lost to the surroundings. (hint: the heat gained by the gold must be equal to the heat lost by the iron.)

Explanation:

The heat released by the iron is absorbed by the gold. This quantity is calculated with the formula , which tells us the amount of heat (energy) Q needed to increase the temperature of a material of mass m, specific heat c by a temperature difference.

Since the heat released (which we will take as negative Q) by the iron (Fe) is absorbed (positive Q then) by the gold (Au) we write , which means , which is to say .

We know that thermal equilibrium has been reached, which means that at the end everything has the same temperature, so we have , and we can substitute and do , to get finally , which means , giving us the final formula .

We can get from tables that and , so we put everything in a calculator and we get