Physics : Specific Heat?

Question

You want to take a bath with the water temperature at 35.0°C. The water temperature is 38.0°C from the hot water tap and 11.0°C from the cold water tap. You fill the tub with a total of 197 kg of water. How many kilograms of water from the hot water tap do you use?

Answer 1

Such problems are solved using the following equation
m(1)ct(1)+m(2)ct(2)=[m(1)+m(2)]ct (1)
where m(1) and m(2) are the masses of the waters you mix, c is the specific heat of water, t(1) and t(2) are the initial temperatures of the waters you mix and t is the temperature of the final mixture.
Solving (1) for m(1) or m(2) you have the solution of the problem. Attention with the units t(Celsius), c(joule/kg) and m(kg)

Answer 2

There is 27 degrees difference between the 2 faucets. The mixed water needs to be 24 degrees warmer than cold faucet.

Answer = (24/27) X 197 Kg

Answer 3

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Total mass of water =197 kg

mass of cold water at 11 C=m kg

mass of hot water at 38 C= ( 197 - m ) kg

Final temperature of 197 kg water =35 C

Principle of heat exchange,

Heat lost = heat gained

(197 -m)*s*(38-35)=m*s*(35-11)

(197 -m)*3=m*24

(197 -m)= 8*m

9*m=197

m=21.889 kg

Mass of hot water=197-21.889=175.111 kg

We use 175.111 kilograms of water from the hot water tap

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