A copper ball of mass 100g is at a temperature T . It is dropped in a copper calorimeter of mass 100g, filled with 170g of water at room temperature, subsequently, the temperature of the system is found to be $75 ° C$ . The value of T is (Given, room temperature = $30 ° C$ , specific heat of copper = $0.1 c a l / g / ° C$ )

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$885 ° C$

$1250 ° C$

$800 ° C$

$825 ° C$

answer is A.

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Detailed Solution

Heat gained (water + calorimeter) = Heat lost by copper ball

$\Rightarrow m_{w} s_{w} Δ T + m_{c} s_{c} Δ T = m_{B} s_{B} Δ T$

$\Rightarrow 170 \times 1 \times (75 - 30) + 100 \times 0.1 \times (75 - 30)$

$\Rightarrow 100 \times 0.1 \times (T - 75) = 885 ° C$

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