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Floating and Sinking

The piece of ...

Question

The piece of zinc at a temperature of $20^{o} C$ weighing $65.38 g$ is dropped into $180 g$ of boiling water ( $T = 100^{o} C$ ). The specific heat of zinc is $0.400 J g^{{- 1}^{o}} C^{- 1}$ and that of water is $4.20 J g^{{- 1}^{o}} C^{- 1}$ . What is the final common temperature reached by both the zinc and water :-

{97.3}^{o} C

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{33.4}^{o} C

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{80.1}^{o} C

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60^{o} C

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Solution

The correct option is A ${97.3}^{o} C$
$m_{Z n} . S_{Z n} . (T_{f} - T_{i}) + m_{H_{2} O} . S_{H_{2} O} . (T_{f} - T_{i}) = 0$

$⟹ (65.38 g m) (0.4 J / g^{o} C) (T_{f} - 20^{o} C) + 180 g m (4.20 J / g^{o} C) \times {(T}_{f} - 100^{o} C) = 0$

$⟹ [(65.38) (0.4) + 180 (420)] T_{f} = (65.38) (0.4) (20) + (180) (4.20) (100)$

$T_{f} = [\frac{(65.38) (0.4) (20) + (180) (4.20) (100)}{(65.38) (0.4) + (180) (4.20)}] = {97.3}^{o} C$

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