A 75 g piece of gold (Au) at 1000 K is dropped into 200 g of H2O at 300K in an insulated container at 1 bar. Calculate the temperature of the system once the equilibrium has been reached. Assume that CP, m for Au and H2O are constant and its value for 298 K throughout the temperature range of interest.

The temperature of the system once the equilibrium has been reached = 372.55K

Explanation:

Heat capacity of gold = 129 J/Kg*c.

Heat capacity of water

4,184 J/Kg*c.

Mass of gold = 75g = 0.075Kg

Mass of water = 200g = 0.2Kg

From conservation of energy

m1*C1 * (t11 - t2) = m2*C2 * (t2 - t21)

Substituting we have

0.075 * 129 * (1000-t2) = 0.2 * 4184 * (t2 - 300) = solving for t2, we have

933.55*t2 = 347790

or t2 = 372.55K

The temperature of the system once the equilibrium has been reached = 372.55K