The rates of cooling of two different liquids put in exactly similar calorimeters and kept in identical surroundings are the same if

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The masses of the liquids are equal

Equal masses of the liquids at the same temperature are taken

Different volumes of the liquids at the same temperature are taken

Equal volumes of the liquids at the same temperature are taken

answer is D.

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Detailed Solution

dTdt=σAmcT4−T04 If the liquids are put in exactly similar calorimeters and identical surrounding then we can consider T0 and A constant. ThendTdt∝T4−T04mc ……(i)If we consider that equal masses of liquids (m) are taken at the same temperature thendTdt∝1cSo for same rate of cooling c should be equal, which is not possible because liquids are of different nature.Again from Eq. (i)dTdt∝T4−T04mc⇒dTdt∝T4−T04VρcNow if we consider that equal volumes of liquids (V) are taken at the same temperature thendTdt∝1ρcSo for same rate of cooling multiplication of ρ×c for two liquids of different nature can be possible. So option (d) may be correct.

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