Heat Transfer
heat diffused in our tuna steak was about 12 mm in 5 minutes. Using these values for L and for t, calculate the value of D for this time point. Enter your answer in cm2/sec, without including the units.
See https://en.wikipedia.org/wiki/Rate_of_heat_flow
Post your work if you get stuck.
The problem states 12 mm for L. Convert to cm to get 1.2 cm and L^2 = 1.2cm*1.2cm = 1.44 cm^2.
Then 1.44 cm^2 = 4D x 300 sec
D = 1.44 cm^2/4*300 sec= 0.0012 cm^2/sec
Explanation
The diffusion equation states that L2=4Dt. Using 1.2 cm and 300 seconds:
1.44 cm2 = 4D x 300 sec
0.0012 cm2/sec = D
This is the explanation.. but I don't understand how to get that Dr Bob
Assuming that is L2 and not L*2, you have D and what's to understand. That's your answer in cm^2/sec.
My Question Dr Bob
how do I get 0.0012 cm2/sec
Which calculation should I do to get that number?
Sorry my clumsiness
Clear enough now.
Thanks Dr Bob
To calculate the value of D (diffusion coefficient) for this time point, we can use the formula for one-dimensional heat conduction:
q = -D * (change in temperature / change in distance)
Where:
q is the rate of heat transfer
D is the diffusion coefficient
(change in temperature) is the difference in temperature across the distance
(change in distance) is the distance over which heat is transferred
In this case, the heat diffused is given as 12 mm in 5 minutes, which means the change in distance is 12 mm and the change in time is 5 minutes. To use consistent units, we convert 12 mm to cm by dividing it by 10.
Using the formula, we rewrite it as:
q = -D * (change in temperature / change in distance)
Rearranging the formula to solve for D:
D = -(q * change in distance) / (change in temperature)
Since the rate of heat transfer (q) is not given in the question, we are unable to calculate the diffusion coefficient (D) without further information.