The time taken for a calorimeter containing 7 | vedclass

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(B) According to Newton's law of cooling,the rate of cooling is proportional to the temperature difference between the body and its surroundings: $\fr

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$15$

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(B) According to Newton's law of cooling,the rate of cooling is proportional to the temperature difference between the body and its surroundings: $\frac{dQ}{dt} = -k(T_{avg} - T_0)$.Since $dQ = (m + x)c \Delta T$,where $x$ is the water equivalent of the calorimeter,we have $(m + x)c \frac{\Delta T}{t} = k(T_{avg} - T_0)$.For the first case: $(75 + x)c \frac{(62 - 58)}{9} = k(T_{avg} - T_0) \implies (75 + x) \frac{4}{9} = K'$ (where $K'$ is a constant).For the second case: $(105 + x)c \frac{(62 - 58)}{12} = k(T_{avg} - T_0) \implies (105 + x) \frac{4}{12} = K'$.Equating the two expressions: $\frac{75 + x}{9} = \frac{105 + x}{12}$.Multiplying both sides by $36$: $4(75 + x) = 3(105 + x)$.$300 + 4x = 315 + 3x$.$x = 315 - 300 = 15 \ g$.

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