A copper sphere of mass 100 g at 100 °C is dropped into 195 g of water at 20 °C held in a copper calorimeter of mass 50 g. Taking specific heat of copper = 0.1 cal/g °C and of water = 1 cal/g °C, the final temperature of the mixture is closest to:

1. Heat lost by copper: $Q = 100 \times 0.1 \times (100 - T) = 10(100 - T)$. 2. Heat gained by water: $Q_1 = 195 \times 1 \times (T - 20)$. 3. Heat gained by calorimeter: $Q_2 = 50 \times 0.1 \times (T - 20) = 5(T - 20)$. 4. Apply $Q = Q_1 + Q_2$: $10(100 - T) = 200(T - 20)$. 5. Expand: $1000 - 10T = 200T - 4000$, so $210T = 5000$. 6. $T = 23.8\ ^\circ C$. Ignoring the calorimeter or mass weighting (e.g. simple average) gives 60 °C, a trap, so it is rejected. _Source: Balbharati (Maharashtra Board) Class 10 Science & Technology, Ch 5 "Heat", p.79_