What is the final temperature of the two pieces of metal in degrees C?

Question

A 356.6g piece of gold (Cp=25.42 J/mol C) was heated to a temperature of -23.4 C and then placed in contact with a 1057g piece of uranium at 78.2 C (Cp=27.67 J/mol C) What is the final temperature of the two pieces of metal in degrees C? Assume no heat is lost into the environment.

Answer 1

Heat lost by the hot metal = heat gained by the colder metal

heat = q = mC∆T where m = mass; C = specific heat; ∆T = change in temperature

Before proceeding, note that mass is given in grams and C is given in J/mole/deg), so we need to change units of mass to moles or change units of moles to grams.

C(uranium) = 27.67 J/mol/deg x 1 mol/238 g = 0.116 J/g/deg

C(gold) = 25.42 J/mol/deg x 1 mol/197 = 0.129 J/g/deg

heat lost by uranium = (1057 g)(0.116 J/g/deg)(78.2 - Tf)

heat gained by gold = (356.6 g)(0.129 J/g/deg)(Tf - -23.4)

Setting these two equal, we have...

(1057 g)(0.116 J/g/deg)(78.2 - Tf) = (356.6 g)(0.129 J/g/deg)(Tf + 23.4)

Solving for Tf we have...

9588 -122.6Tf = 46.0Tf + 1076

168.6Tf = 8512

Tf = 50.5ºC