A swimming pool 20.0m *12.5 is filled with water to a depth of 3.5m. if the initial temperature of water is 18.4C how much heat must be added to the water to raise its temperature to 29.0C? Assume that the density of water is 1.000g/mL
q = mass water x specific heat water x delta T. I would change meters to cm, then volume of the pool of water is height x length x width in cubic centimeters.
To calculate the amount of heat required to raise the temperature of the water in the swimming pool, we can use the formula:
Q = m * c * ΔT
where:
Q = heat energy (in joules)
m = mass of the water (in grams)
c = specific heat capacity of water (in J/g°C)
ΔT = change in temperature (in °C)
First, let's find the mass of the water in the pool. We can find it by multiplying the density of water by the volume of water.
Density = mass/volume
Density of water = 1.000 g/mL
Volume of water = length * width * depth
Volume of water = 20.0 m * 12.5 m * 3.5 m
To convert the volume of water to milliliters, we need to multiply by 1000 (since there are 1000 milliliters in a liter).
Volume of water = (20.0 m * 12.5 m * 3.5 m) * 1000 mL/L
Now, we need to convert milliliters to grams by multiplying by the density of water.
Mass of water = (20.0 m * 12.5 m * 3.5 m) * 1000 mL/L * 1.000 g/mL
Next, we can use the mass of water to calculate the amount of heat required to raise its temperature.
Q = m * c * ΔT
ΔT = final temperature - initial temperature
ΔT = 29.0°C - 18.4°C
Finally, we can substitute the values into the formula and calculate the amount of heat required.
Q = (mass of water) * (specific heat capacity of water) * (change in temperature)