A lizard of mass 3.0 g is warming itself in the bright sunlight. It casts a shadow of 1.6 cm^2 on a piece of paper help perpendicularly to the Sun’s rays. The intensity of sunlight at the Earth is 1.4 x 10^3 W/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 J/(g x C), what is 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 sunlight in order to raise its temperature by 5.0 C?

To solve this problem, we need to use the principles of heat transfer and the specific heat formula. Here's how we can approach each part of the question:

(a) To find the rate of increase of the lizard's temperature, we first need to calculate the amount of energy absorbed by the lizard per second. We can start by finding the power of sunlight absorbed by the lizard.

Power absorbed = Intensity of sunlight × Area of the lizard's shadow

Since only half of the energy penetrates the atmosphere, we need to multiply the intensity by 0.5.

Power absorbed = (0.5 × 1.4 x 10^3 W/m^2) × (1.6 cm^2)

Now, let's convert the lizard's shadow area to square meters:

Area = (1.6 cm^2) × (1 m^2/10^4 cm^2)

Plugging in the values, we have:

Power absorbed = (0.5 × 1.4 x 10^3 W/m^2) × (1.6 cm^2) × (1 m^2/10^4 cm^2)

Simplifying this expression, we get:

Power absorbed = 0.0112 W

Now, we can use the specific heat formula to find the rate of increase of the lizard's temperature:

Rate of temperature increase = Power absorbed / (Mass × Specific heat)

Plugging in the values, we have:

Rate of temperature increase = 0.0112 W / (3.0 g × 4.2 J/(g × °C))

Simplifying this expression, we get:

Rate of temperature increase = 0.0889 °C/s

Therefore, the rate of increase of the lizard's temperature is approximately 0.0889 °C/s.

(b) To find the time required for the lizard to raise its temperature by 5.0 °C, we can use the formula for heat transfer:

Heat = Mass × Specific heat × Temperature change

We need to rearrange this formula to solve for time:

Time = Temperature change / (Rate of temperature increase)

Plugging in the given values, we have:

Time = 5.0 °C / (0.0889 °C/s)

Simplifying this expression, we get:

Time = 56.3 seconds

Therefore, the lizard must lie in the sunlight for approximately 56.3 seconds to raise its temperature by 5.0 °C.