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Heat exchange occurs between three objects. Apply conservation of energy.

An aluminum rod has a mass of 4.5 kg and is initially at room temperature of 23 degrees Celsius. The rod is dropped into an aluminum tank whose mass is 1.22 kg, containing an unknown mass of water. The tank and the water are at 96 degrees Celsius. Heat exchange occurs only between the rod, the tank and the water, all of which end up at 52 degrees Celsius.
Find the mass of the water.
Some constants you may need are:
Thermal capacity of water; cw= 1 calorie per gram per degree C
Thermal capacity of aluminum: ca= .22 cal. per gm. per degree C.

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Physics statements:
A. The thermal capacity of a material is the amount of heat lost or gained when 1 gram of it loses or gains 1 degree Celsius.
B. When ...