A lizard of mass 3.0 g is warming itself in the bright...

A lizard of mass $3.0 \mathrm{g}$ is warming itself in the bright sunlight. It casts a shadow of $1.6 \mathrm{cm}^{2}$ on a piece of paper held perpendicularly to the Sun's rays. The intensity of sunlight at Earth is $1.4 \times 10^{3} \mathrm{W} / \mathrm{m}^{2},$ but only half of this energy penetrates the atmosphere and is absorbed by the lizard. (a) If the lizard has a specific heat of $4.2 \mathrm{J} /\left(\mathrm{g} \cdot{ }^{\circ} \mathrm{C}\right),$ what is the rate of increase of the lizard's temperature? (b) Assuming that there is no heat loss by the lizard (to simplify), how long must the lizard lie in the Sun in order to raise its temperature by $5.0^{\circ} \mathrm{C} ?$

Key Concepts

Energy Absorption and Effective Irradiance

Not all the incident light energy is absorbed by an object; factors such as atmospheric absorption can reduce the effective energy that reaches and is absorbed by the object. Here, only a fraction (half) of the solar intensity contributes to an increase in the lizard's energy, emphasizing the importance of considering efficiency or loss factors in energy transfer problems.

Specific Heat Capacity

Specific heat capacity is a property that relates the amount of energy required to raise the temperature of a unit mass of a substance by one degree. This concept is essential for determining how much energy must be absorbed to achieve a given temperature rise, linking energy input (from absorbed sunlight) to the resulting temperature change.

Radiant Energy and Intensity

This concept involves understanding how energy is carried by electromagnetic radiation, quantified as intensity (power per unit area). In this context, it explains how sunlight delivers energy to a surface, which is critical for calculating the amount of energy incident on an object based on its exposed area.

Rate of Temperature Increase

This key concept connects the rate of energy absorption (power) to the specific heat and mass of the object, establishing how quickly the temperature increases. By calculating the energy absorbed per unit time and comparing it to the energy required to increase the temperature by a specific amount, it is possible to determine the rate of temperature rise and the time needed for a certain temperature change.

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