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  4. A copper ball of mass 100 gm is at a temperature T. It is dropped in a copper calorimeter of mass 100 gm, filled with 170 gm of water at room temperature. Subsequently, the temperature of the system is found to be 75° C. T is given by: (Given: room temperature = 30°C, specific heat of copper = 0.1 cal g-1 ° C-1)

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Q. A copper ball of mass $100\, gm$ is at a temperature $T$. It is dropped in a copper calorimeter of mass $100\, gm$, filled with $170\, gm$ of water at room temperature. Subsequently, the temperature of the system is found to be $75^{\circ} C$. $T$ is given by :
(Given : room temperature = $30^{\circ}C$, specific heat of copper = $0.1\, cal\,g^{-1}\,{}^{\circ} C^{-1}$)

JEE MainJEE Main 2017Thermal Properties of Matter

Solution:

$100 \times 0.1 \times (t - 75) = 100 \times 0.1 \times 45 + 170 \times 1 \times 45$
$10t - 750 = 450 + 7650$
$10t = 1200 + 7650$
$10t = 8850$
$t = 885^{\circ} C$