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?
What is your question about this?
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?
I think you might be answer grazing.
HeatLizardabsorbs=.5 heat sun
mass*c*deltaTemp=.5*Intensity*area*time
deltaTemp/time= you do the math.
then for part b, calculate time for a deltaTemp of 5.
deltaTEmp/time known in part a.
part a= 5C/time calculate time
To solve this problem, we need to consider the amount of energy absorbed by the lizard and use the given information to calculate the rate of temperature increase and the time required for a specific temperature increase.
(a) To determine the rate of increase of the lizard's temperature, we need to calculate the amount of energy absorbed by the lizard per second.
The energy absorbed per second can be calculated by multiplying the intensity of sunlight (after passing through the atmosphere) by the area of the lizard's shadow:
Energy absorbed per second = (1/2) x (intensity of sunlight) x (area of shadow)
First, let's convert the intensity of sunlight from W/m^2 to J/s/m^2 by multiplying it by 1 since 1 W = 1 J/s:
Intensity of sunlight = 1.4 x 10^3 J/s/m^2
Next, convert the lizard's shadow area from cm^2 to m^2:
Area of shadow = 1.6 cm^2 = (1.6 x 10^(-4)) m^2
Substituting the values into the formula:
Energy absorbed per second = (1/2) x (1.4 x 10^3 J/s/m^2) x (1.6 x 10^(-4)) m^2
Now, multiply the energy absorbed per second by the mass of the lizard to find the rate of increase of the lizard's temperature:
Rate of increase of temperature = (Energy absorbed per second) / (mass of the lizard)
Mass of the lizard = 3.0 g = 3.0 x 10^(-3) kg
Substituting the values:
Rate of increase of temperature = [(1/2) x (1.4 x 10^3 J/s/m^2) x (1.6 x 10^(-4)) m^2] / (3.0 x 10^(-3) kg)
Simplify the expression and calculate the rate of increase of temperature.
(b) To determine the time required for the lizard to raise its temperature by 5.0 C, we can use the specific heat formula:
Energy absorbed = (mass of the lizard) x (specific heat) x (temperature increase)
First convert the lizard's mass from grams to kilograms:
Mass of the lizard = 3.0 g = 3.0 x 10^(-3) kg
Now substitute the values into the formula:
Energy absorbed = (3.0 x 10^(-3) kg) x (4.2 J/(g x C)) x (5.0 C)
To calculate the time required, we need to divide the energy absorbed by the energy absorbed per second calculated in part (a):
Time required = (Energy absorbed) / (Energy absorbed per second)
Substitute the values, simplify the expression, and calculate the time required.