A snake is sunning itself on a rock. (a) If the snake is 0.3 m long, what is the approximate amount of radiation it absorbs from the sun in 10 minutes? (b) If no heat flows out of the snake via conduction or by evaporative cooling, how much does its temperature increase during 10 min? Assume all the sun’s energy goes into heating the snake and the specific heat of the snake is equal to the specific heat of water
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To answer these questions, we need to use two formulas: one for calculating the amount of radiation absorbed by an object from the sun and another for calculating the change in temperature of an object due to absorbing energy.
(a) To calculate the amount of radiation absorbed by the snake from the sun, we can use the formula:
Q = A * ε * σ * ΔT
where:
Q is the amount of radiation absorbed (in Joules),
A is the surface area of the snake (in square meters),
ε is the emissivity of the snake (a dimensionless quantity between 0 and 1),
σ is the Stefan-Boltzmann constant (approximately 5.67 x 10^-8 W/(m^2K^4)),
ΔT is the change in temperature (in Kelvin).
Since we have the length of the snake (0.3 m), we can assume it has a cylindrical shape, and the surface area A can be calculated as:
A = 2πrh + πr^2
where:
r is the radius of the snake (which we can assume to be small compared to its length),
h is the height of the snake (0.3 m).
(b) To calculate the change in temperature of the snake, we can use the formula:
ΔT = Q / (m * c)
where:
ΔT is the change in temperature (in degrees Celsius),
Q is the amount of energy absorbed (in Joules, which we can calculate in part (a)),
m is the mass of the snake (which we can assume to be proportional to its length),
c is the specific heat capacity of the snake (which is given to be equal to the specific heat of water).
Now, let's plug in the values and calculate the answers.
(a) Calculating the amount of radiation absorbed by the snake:
1. Calculate the surface area A using the formula mentioned above.
2. Assume a value for the emissivity of the snake (this depends on the type of material the snake's skin is made of).
3. Plug in the values into the formula Q = A * ε * σ * ΔT, where we assume ΔT is the change in temperature (in Kelvin) during the 10 minutes.
(b) Calculating the change in temperature of the snake:
1. Calculate the mass of the snake as a proportional value based on its length.
2. Use the formula ΔT = Q / (m * c), where we can assume m is the mass of the snake and c is the specific heat capacity of water.
By following these steps, you can find approximate answers to both questions. Note that these calculations are based on assumptions, and the actual values may vary in real-world scenarios.