When you take a bath, how many kilograms of hot water (51°C) must you mix with cold water (12°C) so that the t?
When you take a bath, how many kilograms of hot water (51°C) must you mix with cold water (12°C) so that the temperature of the bath is 36°C? The total mass of water (hot plus cold) is 190 kg. Ignore any heat flow between the water and its external surroundings.
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heat gain/loss is given by Q= m c delta T
where m is the mass, c the specific heat and delta T the change in temp
call m1 the mass of the cold water and m2 the mass of the warm water, we know that
m1+m2=190 or m1=190-m2
the cold water gains an amount of energy = m1 c (36-12) = (190-m2)(c)(24)
the warm water loses an amount of energy = m2 c (51-36) =15 m2 c
equate these:
15m2 = 24(190-m2)
m2=116.9kg so m1=190-m2=73.1kg