A 0.10 kg piece of copper at an initial temperature of 95°c is dropped into 0.20 kg of water contained in a 0.28 kg aluminum calorimeter. the water and calorimeter are initially at 15°c. what is the final temperature of the system when it reaches equilibrium? show your work.

(cp of Copper = 387J / kg times degrees C; cp of Aluminum = 899 J / kg times degrees C; cp of Water = 4186J / kg times degrees C)

Use the law of conservation of energy and assuming no heat loss to the surroundings, then

Heat given up by copper = heat absorbed by water + heat absorbed by calorimeter

Working formula is

Q = heat = MCp (delta T)

where

M = mass of the substance

Cp = specific heat of the substance

delta T = change in temperature

Heat given up by copper = 0.10 (387) (95 - T)

Heat absorbed by water = 0.20 (4186) (T - 15)

Heat absorbed by calorimeter = 0.28 (899) (T - 15)

where

T = final temperature of the system

Substituting appropriate values,

0.10 (387) (95 - T) = 0.20 (4186) (T - 15) + 0.28 (899) (T - 15)

38.7 (95 - T) = 1088.92 (T - 15)

3676.50 - 38.7T = 1088.92T - 16333.8

1127.62T = 20010.3

T = 17.75 C