Calculating Specific Heat Capacity of Oil-Water Mixture

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i am not sure if my question fits in this place.

if i have certain amounts of water and oil, 3kg and 4kg.
i mix them together, and i want to find the specific heat capacity of the mixture, according to my book the specific heat capacity of such a mixture is the sum of the two specific heat capacities of the liquids.

this does not really make any sense to me, if i put heat into the mixture shouldn't the water or the oil part of the mixture take longer to heat up?
does the heat transfer not depend on the heat capacity individually?
certain parts of the mixture are made of oil and water and therefore supposed to have different heat capacities, and yet when you put them into a mixture they all have the same heat capacity.
 
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Yes, the mixture has ONE heat capacity. While it may take different amounts of heat to raise the oil droplets and the water through a given change in temperature, you must accept that in equilibrium (ie: given enough time), the two phases reach the same temperature (by exchanging heat with each other).
 
Think in terms of mixture being black box seen from the outside - you don't see individual components being heated.