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The temperature of a body raises by $44 ° C$ when a certain amount of heat is given to it. The same heat when supplied to $22 g$ of ice at $- 8 ° C,$ raises its temperature to $16 ° C .$ The water equivalent of the body in grams is____________ (Given data $S_{w a t e r} = 1 c a l / g ° C$ and $L_{f} = 80 c a l / g, S_{i c e} = 0.5 c a l / g ° C$ )

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answer is 50.

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Detailed Solution

$Q = m_{I} S_{I} Δ θ + m_{I} L_{f} + m_{W} s_{W} Δ θ$

$Q = 22 \times 0.5 \times (8) + 22 \times 80 + 22 \times 1 \times 16$

$Q = 2200 c a l \to (1)$

Heat required to raise the temperature of the body by $44 ° C$

$Q = m s Δ θ = m s (44) \to (2)$

From $(1) & (2), m s (44) = 2200$

$∴$ Water equivalent of the body $(m s) = \frac{2200}{44} = 50 g$

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