A swimming pool with a surface area of 5
meters by 10 meters contains 88,000 liters of
water. The temperature of the water in this
pool increases by 2.00 C when it is heated by
the Sun for 6.00 hours. Calculate the energy absorbed.
1.1.48×109J
2.2.22×109J
3.7.4×108J
4.3.7×108J
7.4 x 108j
To calculate the energy absorbed by the water in the pool, we can use the specific heat capacity formula:
Q = mcΔT
Where:
Q = energy absorbed (in Joules)
m = mass of the water (in kilograms)
c = specific heat capacity of water (4.186 J/g°C)
ΔT = temperature change (in °C)
First, we need to calculate the mass of the water in the pool. We know that 1 liter of water is equivalent to 1 kilogram, so the mass of the water in the pool is 88,000 kg.
Next, we need to calculate the temperature change, which is 2.00°C.
Now, substituting these values into the formula:
Q = (88,000 kg) * (4.186 J/g°C) * (2.00°C)
Q = 736,448 J
Therefore, the energy absorbed by the water in the pool is approximately 736,448 Joules.
The closest option to this value is option 3: 7.4 × 10^8 J.
To calculate the energy absorbed by the water in the pool, we can use the formula:
Energy absorbed = Mass of water * Specific heat capacity * Change in temperature
Firstly, we need to calculate the mass of water in the pool using the density formula:
Density = Mass / Volume
Since the volume is given in liters, we know that 1 liter of water has a mass of 1 kilogram (kg) because the density of water is 1 kg/L. Therefore, we have:
Mass = Volume * Density
Mass = 88,000 * 1
Mass = 88,000 kg
Next, we need to determine the specific heat capacity of water. The specific heat capacity of water is 4.18 kJ/kg°C.
Now, we can calculate the energy absorbed:
Energy absorbed = Mass of water * Specific heat capacity * Change in temperature
Energy absorbed = 88,000 kg * 4.18 kJ/kg°C * 2.00°C
Energy absorbed = 734,560 kJ
To convert this to joules (J), we multiply by 1000:
Energy absorbed = 734,560 kJ * 1000
Energy absorbed = 734,560,000 J
From the given options, the closest answer is 734,560,000 J, which corresponds to option 3.7.4×108J.