Final answer:
To raise the bath's temperature from 15°C to 35°C using 60°C water, you would need to add 80 liters of the hot water, according to the heat balance principle.
Step-by-step explanation:
To find out how much water at 60°C needs to be added to the bath to raise the water temperature to 35°C, you can use the concept of heat balance. Since there is no phase change and we can ignore heat losses to the environment, the heat gained by the cold water should be equal to the heat lost by the hot water.
Let m1 be the mass of the water already in the bath (100 liters), t1 its initial temperature (15°C), m2 the mass of the hot water added (unknown), t2 its temperature (60°C), and t f the final temperature of the mixture (35°C).
The equation for heat gained or lost is Q = mcΔT, where m is mass, c is the specific heat capacity (which is 4.186 J/g°C for water), and ΔT is the change in temperature.
Since the specific heat capacity of water is constant, it can be omitted from our calculations when dealing with the same substance. We can set up the equation as follows:
m1 * (t f – t1) = m2 * (t2 – t f)
Simplifying the numbers:
100 * (35 – 15) = m2 * (60 – 35)
2000 = m2 * 25
m2 = 2000 / 25
m2 = 80 liters
Therefore, 80 liters of water at 60°C needs to be added to the bath.