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Specific Heat Capacity

Select the co...

Question

Select the correct option given below:
When $1.5 k g$ of ice at $0^{o} C$ mixed with $2 k g$ of water at $70^{o} C$ in a container, the resulting temperature is $5^{o} C$ the heat of fusion of ice is $(s_{w a t e r} = 4186 J K g^{- 1} K^{- 1})$

1.42 \times 10^{5} J k g^{- 1}

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2.42 \times 10^{5} J k g^{- 1}

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3.42 \times 10^{5} J k g^{- 1}

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4.42 \times 10^{5} J k g^{- 1}

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Solution

The correct option is C $3.42 \times 10^{5} J k g^{- 1}$
Heat lost by water $= m_{w} s_{w} (T_{2} - T_{f})$
$= 2 \times 4186 \times (70 - 5) = 544180 J$

Heat required to melt ice $= m_{i} L_{f} = 1.5 \times L_{f}$

Heat required to rise temperature of ice
$\Rightarrow m_{i} s_{w} (T_{f} - T_{0}) = 1.5 \times (4186) \times (5 - 0^{o}) = 31395 J$

By the principle of calorimetry
heat lost = heat gained
$544180 = 1.5 L_{f} + 31395$

$∴ L_{f} = \frac{512785}{1.5} = 341856.67 = 3.42 \times 10^{5} J k g^{- 1}$

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100 g m

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= 0.42 \times 10^{3} J k g^{- 1} K^{- 1}

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