In order to determine a newly developed material\'s specific heat conduct, mater

Question

In order to determine a newly developed material's specific heat conduct, material scientists conduct an experiment. First, they place a chunk of the object (a mass of 100 grams) into boiling water until it's in thermodynamic equilibrium with the boiling water. Next, the object is taken from the biling water and dropped into a perfectly insulated aluminum container of 300 grams that already contains 100 grams of water initially, and the water and aluminum container have a temperature of 25 degrees Celsius. If the final temperature after the object is added rises to 50 degrees Celsius, what is the specific heat of the unknown?

Explanation / Answer

Mass of object = 0.1 kg

Block is in equilbrium with boiling water i.e. @100 C => initial block temp is 100 C

Mass of Al container = 0.3 kg . mass of water in it = 0.1kg . temp = 25 C

Specific heat of water = 4.18 kJ/kg C

Specific heat of Al = 0.9kJ/kg C (taken from data table, as not provided in question)

Final temp of container with water & object = 50 C

As perfectly insulated container => no heat loss

Writing heat balance equation. heat lost by hot object = heat gained by cold Al container & the water

=> (0.1)(C)(100-50) = (0.1)(4.18)(50-25) + (0.3)(0.9)(50-25)

=> 5 C = 17.2

=> C =3.44 kJ/kg C (ans)

The specific heat of unknown substance is 3.44 kJ/kg C

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