Question

What would be the appropriate equilibrium temperature of a system obtained by adding 25.0 g of ice at 0°C to 250.0 mL of "hot" (80°C) coffee, assuming that the heat capacity and density of the coffee are the same as for pure water (4.18 J g-1 °C-1 and 0.997 g mL-1), and also assuming negligible heat transfer with the surroundings? [For water, ΔHfusion = 6.02 kJ/mol.]   

*Note: the answer is 65 deg C

Answer 1

First, let's list all the heat transfer which can occur in the ystem.

=heat absorbed y the ice to melt at 0⁰ C

=heat absorbed by the melted ice to warm from 0 to T⁰ C

=heat released from coffee to cool from 80⁰ C to T⁰ C

Now write equations for each of the identified heat transfers in the system.

Now,since there is no heat loss,