Mrs. Wilson leaves her freshly-baked blueberry pie on the windowsill to cool. The delicious fragrance diffuses through the air with a diffusion coefficient of D = 0.2 cm2/s.
How long does it take for Dennis to smell the pie in his treehouse 10 meters away? Give your answer in days, without entering the unit.
Could you please help me to solve this problem?
1000^2 / 4 * 0.2
I think it's x^2/2D or 1000^2/0.4
See this calculator
https://www.physiologyweb.com/calculators/diffusion_time_calculator.html
t = L^2 / 4D
D = 0.2cm^2 / sec
L = 10 meters or 1000cm
t= 1000^2 / 4 (0.2)
Solve then convert seconds into days.
Hint : The answer is more than 10 days :)
Certainly! To solve this problem, we can use Fick's Law of Diffusion, which relates the rate of diffusion to the concentration gradient and the diffusion coefficient.
The equation for Fick's Law of Diffusion is as follows:
Rate of diffusion = (Diffusion coefficient * Area * Concentration gradient) / Thickness
In this case, the concentration gradient is the difference in concentration between the windowsill where the pie is and the treehouse where Dennis is located, and the thickness is the distance between them.
We are given that the diffusion coefficient (D) is 0.2 cm2/s, the distance (thickness) is 10 meters, and we are looking for the time it takes for Dennis to smell the pie, so we can rearrange the equation as follows:
Time = (Thickness^2 * Concentration gradient) / (Diffusion coefficient * Area)
To calculate the concentration gradient (C), we need to convert the distance from meters to centimeters (1 meter = 100 centimeters). Therefore, the distance is 1000 centimeters.
Now, let's calculate the concentration gradient.
Concentration gradient = (Concentration at the windowsill - Concentration at the treehouse) / Thickness
Since the concentration at the treehouse is zero (Dennis cannot smell the pie yet), we can simplify the equation:
Concentration gradient = Concentration at the windowsill / Thickness
Now, let's plug in the values for the remaining variables:
Concentration gradient = 1 / 1000 centimeters
Now, substitute the values into the equation for Time:
Time = (10^2 * (1 / 1000)) / (0.2 * Area)
However, we haven't been given the area of diffusion. Without the area, we cannot directly calculate the time it takes for Dennis to smell the pie.
If you have the specific area of diffusion or any other additional information, please provide it so we can proceed with the calculation.