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A copper sphere of mass 100 g is initially at temperature T. It is placed into a copper calorimeter of mass 100 g containing 170 g of water initially at room temperature. After thermal equilibrium is reached, the final temperature of the whole system is 75°C. Find T. [Given: room temperature = 30°C, specific heat of copper = 0.1 cal/g°C]

1. 1250°C
2. 825°C
3. 800°C
4. 885°C

Correct answer: 885°C

Solution

Heat lost by copper sphere = heat gained by water and calorimeter: 100*0.1*(T-75) = 170*1*(75-30) + 100*0.1*(75-30). So 10*(T-75) = 7650 + 450 = 8100, giving T - 75 = 810, T = 885 C.

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