A water heater is operated by solar power. If the solar...

A water heater is operated by solar power. If the solar collector has an area of 6.00 $\mathrm{m}^{2}$ and the intensity delivered by sunlight is $550 \mathrm{W} / \mathrm{m}^{2},$ how long does it take to increase the temperature of 1.00 $\mathrm{m}^{3}$ of water from $20.0^{\circ} \mathrm{C}$ to $60.0^{\circ} \mathrm{C} ?$

Key Concepts

Power-Energy-Time Relationship

Power is defined as the rate at which energy is transferred or converted, and is expressed as energy divided by time. By knowing the energy required to heat the water and the power supplied by the solar collector, one can calculate the time required for heating using the relationship t = energy/power.

Solar Energy Collection

This concept pertains to how solar energy is captured using a collector with a specific area. The power incident on the collector is determined by the product of its area and the solar energy intensity, which then dictates the rate at which energy is gathered.

Mass-Density Conversion

Often in thermal problems, the volume of a liquid is provided but calculations require the mass. Knowing the density (mass per unit volume) of a substance like water allows for the conversion of volume to mass, which is essential for computing the energy required using the specific heat capacity.

Energy Conservation and Transfer

This concept involves calculating the energy needed for a temperature increase by multiplying the mass of the substance, its specific heat capacity, and the temperature change. It is rooted in the principle that the energy provided must equal the increase in the internal energy of the substance, assuming no losses.

Specific Heat Capacity

This is a fundamental property that indicates the amount of thermal energy required to raise the temperature of a unit mass of a substance by one degree Celsius (or Kelvin). In thermal energy problems involving heating substances like water, it is used to calculate the total energy required to achieve a desired temperature change.

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