A swimming pool, 20.0 m 12.5 m, is filled with water to a depth of 3.73 m. If the initial temperature of the water is 18.5°C, how much heat must be added to the water to raise its temperature to 28.5°C? Assume that the density of water is 1.000 g/mL.
I would change the dimensions to cm, then h x w x l = volume in cc.
That many cc will be that many grams H2O.
Then q = mass H2O in grams x specific heat H2O in J/g (or cal/g) x (Tfinal-Tinitial).
To calculate the amount of heat required to raise the temperature of the water in the swimming pool, you can use the formula:
Q = m × c × ΔT
Where:
Q is the amount of heat (in Joules)
m is the mass of the water (in grams)
c is the specific heat capacity of water (4.184 J/g°C)
ΔT is the change in temperature (in °C)
Step 1: Calculate the mass of the water in the swimming pool
To find the mass of the water, we can use the formula:
mass = density × volume
Given:
density of water = 1.000 g/mL
volume of the pool = length × width × depth
Calculating the volume of water:
Volume = 20.0 m × 12.5 m × 3.73 m = 930.125 m³
Converting the volume to mL:
Volume = 930.125 m³ × 10^6 = 930,125,000 mL
Calculating the mass:
mass = density × volume = 1.000 g/mL × 930,125,000 mL = 930,125,000 g
Step 2: Calculate the change in temperature
ΔT = final temperature - initial temperature = 28.5°C - 18.5°C = 10°C
Step 3: Calculate the amount of heat
Q = mass × specific heat capacity × ΔT
Q = 930,125,000 g × 4.184 J/g°C × 10°C
Calculating:
Q = 38,807,212,500 J
Therefore, approximately 38,807,212,500 Joules of heat must be added to the water in the swimming pool to raise its temperature from 18.5°C to 28.5°C.
To find the amount of heat required to raise the temperature of the water in the swimming pool, we need to consider the following steps:
Step 1: Calculate the mass of the water.
Step 2: Find the specific heat capacity of water.
Step 3: Use the equation Q = mcΔT to calculate the heat.
Step 1: Calculate the mass of the water:
The volume of the swimming pool can be found by multiplying the length, width, and depth of the pool:
Volume = Length × Width × Depth
= 20.0 m × 12.5 m × 3.73 m
= 932.5 m³
Since the density of water is 1.000 g/mL (which is equivalent to 1,000 kg/m³), we can calculate the mass of the water:
Mass = Volume × Density
= 932.5 m³ × 1,000 kg/m³
= 932,500 kg
Step 2: Find the specific heat capacity of water:
The specific heat capacity of water is the amount of heat energy required to raise the temperature of 1 gram of water by 1 degree Celsius.
The specific heat capacity of water is approximately 4.18 J/g°C (joules per gram per degree Celsius).
Step 3: Use the equation Q = mcΔT to calculate the heat:
Q = mcΔT
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, convert the mass of the water from kilograms to grams:
Mass (g) = 932,500 kg × 1,000 g/kg
= 932,500,000 g
Now, calculate the heat energy required using the equation Q = mcΔT:
Q = (Mass) × (Specific heat capacity) × (Change in temperature)
= 932,500,000 g × 4.18 J/g°C × (28.5°C - 18.5°C)
Simplifying,
Q = 932,500,000 g × 4.18 J/g°C × 10°C
Multiplying,
Q = 38,878,150,000 J
Therefore, approximately 38,878,150,000 joules of heat must be added to the water to raise its temperature from 18.5°C to 28.5°C.