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Unknown metal of mass 192 g heated to a temperature of $100^{0} C$ was immersed into a brass calorimeter of mass 128 g containing 240 g of water at a temperature of ${8.4}^{0} C .$ Calculate the specific heat of the unknown metal, if water temperature stabilizes at ${21.5}^{0} C .$ (Take, specific heat of brass is 394 $J k g^{- 1} K^{- 1})$

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916 $J k g^{- 1} K^{- 1}$

654 $J k g^{- 1} K^{- 1}$

1232 $J k g^{- 1} K^{- 1}$

458 $J k g^{- 1} K^{- 1}$

answer is A.

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Detailed Solution

Principle of Calorimetry

$\begin{array}{l} 192 \times S \times (100 - 21.5) \\ = 128 \times 394 \times (21.5 - 8.4) \\ + 240 \times 4200 \times (21.5 - 8.4) \\ \Rightarrow S = 916 J k g^{- 1} K^{- 1} \end{array}$

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