A circular lake 1.0 km in diameter is 10 m deep. Solar energy is incident on the lake at an av

step 1 As we all know that the expression for p is equal to Q by T and also I can write the value of p

A circular lake 1.0 km in diameter is 10 m deep. Solar...

A circular lake $1.0 \mathrm{~km}$ in diameter is $10 \mathrm{~m}$ deep. Solar energy is incident on the lake at an average rate of $200 \mathrm{~W} / \mathrm{m}^{2}$. If the lake absorbs all this energy and doesn't exchange energy with its surroundings, how much time is required to raise the temperature from $5^{\circ} \mathrm{C}$ to $20^{\circ} \mathrm{C} ?$

Key Concepts

Specific Heat Capacity and Energy to Raise Temperature

This concept involves calculating the amount of energy needed to increase the temperature of a substance based on its mass, specific heat capacity, and the desired temperature change. The fundamental relation Q = m * c * ?T lays the foundation for solving problems where thermal energy must be supplied to a system.

Volume and Mass Determination

Determining the total mass of a substance from its volume and density is a key step in many energy transfer problems. For fluids, the volume is often computed from geometric dimensions (such as area and depth), and then the density is used to convert this volume into mass, which is critical for subsequent energy calculations.

Solar Irradiance and Energy Flux

Solar irradiance refers to the power per unit area received from the sun. When applied to a surface, multiplying the irradiance by the surface area gives the total energy input per unit time. This concept is central to understanding how environmental energy sources contribute to the heating of systems.

Energy Conservation and Time Calculation

The principle of energy conservation states that the energy absorbed by a system will result in a temperature change based on the system's specific heat capacity and mass. By equating the rate of energy input (from sources like solar irradiance) to the energy required for a specified temperature increase, one can calculate the time needed to achieve that thermal change.

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