What is the original temperature of the mercury?

Question

as a 5.00-kg sample of liquid mercury is cooled into a solid, it liberates 157 kJ of energy.

For mercury, the melting point is 234 K, the heat of fusion is 11.3 kJ/kg, and the specific heat is 140 J/kg • K.

Answer 1

157 kJ is the total energy liberated in going from liquid mercury to solid mercury.  There are 2 steps in this conversion.

First, the 5.00 kg (5000 g) is cooled from the initial temperature (which is unknown) down to its freezing/melting point (234 K).  Next, a phase change occurs in going from liquid to solid (no change in temperature).  So, to find the initial temperature, we can work backwards.

Heat liberated during phase change = mass x ∆Hfus = 5.00 kg x 11.3 kJ/kg = 56.5 kJ

Heat liberated during cooling from initial temperature down to 234 K = 157 kJ - 56.5 kJ = 100.5 kJ

Heat liberated during cooling = 100.5 kJ = q = mC∆T were m = mass; C = specific heat; ∆T = change in temperature

q = (5.00 kg)(0.140 kJ/kg/deg)(∆T) = 100.5 kJ

∆T = 144 degrees 

Initial temperature = 234 K + 144 K = 378 K