Question

What will be the equilibrium temperature when a 275 g block of copper at 235 ?C is placed in a 135 g aluminum calorimeter cup containing 875 g of water at 14.0 ?C?

Answer 1

The value of specific heat for copper is 390 J/kg?C?, for aluminun is 900 J/kg?C?, and for water is 4186 J/kg?C?.

Cu = 0.275 Kg, Al = 0.135Kg , H2O = 0.875 Kg

The initial temperature of the aluminum and water is 14?. When the copper is placed in the cup, the temperature of the copper will decrease as the temperature of the aluminum and water increases. Use the following equation to determine the heat released by the copper.

Q = m * Specific heat * (Ti – Tf)
Q = 0.275 * 390 * (235 – Tf) = 25,203.75 – 107.25 * Tf

Use the following equation to determine the heat absorbed by the aluminum and water.
Q = m * Specific heat * (Tf – Ti)

For Al, Q = 0.135 * 900 * (Tf – 14) = 121.5 * Tf – 1701
For H2O, Q = 0.875 * 4186 * (Tf – 14) = 3662.75 * Tf – 51,278.5
Total heat absorbed = 121.5 * Tf – 1701 + 3662.75 * Tf – 51,278.5 = 3784.25 * Tf – 52,979.5

Total heat absorbed = heat released

3784.25  * Tf – 52,979.5 = 25,203.75 – 107.25 * Tf
3891.5 * Tf = 78,183.25
Tf = 78,183.25 / 3891.5 = 20.09 ?C

Hence Equillibrium temperature is 20.09 ?C.