A water heater is operated by solar power. If solar collector has an area of 6.00m^2, and the intensity

delivered by sunlight is 550W/m^2, how long does it take to increase the temperature of 1m^3 of water from
20°Cto 60°C?

To calculate the time it takes to increase the temperature of 1m^3 of water from 20°C to 60°C using a solar-powered water heater, we need to consider the amount of heat energy required to heat the water and the amount of energy delivered by the solar collector.

First, let's calculate the energy required to heat the water using the specific heat capacity equation:

Q = mcΔT

Where:
Q = heat energy
m = mass of water (1m^3 = 1000kg, as 1 liter of water weighs 1 kg)
c = specific heat capacity of water (approximated to 4.18 J/g°C since the density of water is approximately 1 g/mL)
ΔT = change in temperature (60°C - 20°C = 40°C)

Now, let's calculate the energy required to heat 1m^3 of water:

m = 1000kg
c = 4.18 J/g°C = 4180 J/kg°C
ΔT = 40°C

Q = (1000kg) * (4180 J/kg°C) * (40°C)
Q = 1.672 × 10^8 J

Next, let's calculate the energy delivered by the solar collector. We can do this by multiplying the intensity of sunlight (550 W/m^2) by the area of the solar collector (6.00m^2):

Energy delivered = intensity * area
Energy delivered = 550 W/m^2 * 6.00m^2
Energy delivered = 3,300 W

Now, let's calculate the time it takes to deliver the required energy to heat the water:

Time = Energy delivered / Rate
Time = 1.672 × 10^8 J / 3,300 W

Converting the energy from Joules to kilowatt-hours (kWh) for consistency:

1 kWh = 3.6 × 10^6 J

Time = (1.672 × 10^8 J) / (3,300 W) * (1 kWh / 3.6 × 10^6 J)

Now, let's solve for Time:

Time = (1.672 × 10^8 J) / (550 W) * (1 kWh / 3.6 × 10^6 J)
Time ≈ 8.07 hours

Therefore, it would take approximately 8.07 hours to increase the temperature of 1m^3 of water from 20°C to 60°C using a solar-powered water heater with a solar collector of 6.00m^2 area and a sunlight intensity of 550W/m^2.