So... If I took two points from the simulated transient response of a first order system to withing 6 dec digits and rephrased the problem using these values you would have got the answer ??
fack no, you don't even know the basics of the worlds most simple differential equation. But you do know how to run your little keyboard mouth.
Ah yeah it is a brilliant problem aint it. And on the plus side it was triggered by actual experience. I was cooking a roast and after taking two readings got to thinking about how to use that data to project the done time so i didn't have to check so often. I might even code it up and put it in a micro controller with a display showing current temp and estimated done time. As a side not hawcreek is done as a board scientist
Some of you RWNJ would be the first to land there. Your opinions are ignorant and driven by idealistic fervor.
Cause I picked the numbers to be close not exact. And no they do not plot an ess curve you idiot.
Do you think you could plot
T(t) = 261*(1 - exp(-0.004435 * t))
T(50) = 86.96
T(100) = 128
Not terribly off for just picked numbers. Don't bother you can't understand.
Yeah I understand you are a little miffed what with you not being able to make a single relevant comment and not even understanding the solution of the most basic differential equation known to man and really not even understanding the reason for its use.
Tried to post the code that solved it but this ignorant web site won't allow.
Answer is 47 more minutes that Andrew will have to endure his fathers bee yatching.
The first order system is the solution of the differential equation.
DT/Dt = K*(Tf - T)
T = roast temperature
t = time
Tf = Oven internal temp ( not needed to solve the problem, comes out of the data points )
Ti = Initial roast temperature at time zero
The solution form is the exponential.
T(t) = Tf( 1 - exp(-tau*t))
But not knowing the oven temp how can this be solved ??
Knowing two points during cooking allows solving one equation for Tf then substituting back into the other.
If you work the algebra you get.
(T2 - Ti)/(T1 - Ti) = ( 1 - exp(-tau*t1))/(1 - exp(-tau*t2))
"Because it makes your problem unsolvable in the real world, that's pretty simple actually."
Here I fixed it for you.
""Because it makes your problem unsolvable by a nitwit like me, that's pretty simple actually.""
why does the rate changing between periods bother you. Let me guess you still haven't looked up "first order system".
Do you realize that you are embarrassing yourself.
how many data points does one need to find the unknowns in an exponential response.
Y(t) = K*(1-exp(-tau*t))
Huh dum dum ...
You say nothing to prove yourself any better. Just idle insults and inane blabber. Tell me what is wrong with the question in detail if you claim to have any ability. And first there IS a difference between a "first order model" and "first order system" look it up on Google before you reply. So far I think a third party would justly conclude you are mouthy blowhard who is incapable of feeling shame.
It's a simple case of finding the best time constant for the solution given the measured points. Then solving for the time at which the system will be at 160F. Hawfaeces has answered so we have 1 fail and 0 correct.
Do you find it ironic that you cast insults about math ability while clearly failing to understand much less answer the question in the same thread. I am done with you on this one, you failed yet again. I will give others some chance and then post the answer.
No backtracking you moron.
the problem stated "first order system"
You misunderstood the problem due to lack of knowledge.
The problem is very well posed for anyone who has had freshman calculus.
I don't think you ever got an engineering degree. You confused two things.
"first order model"
"first order system"
If you have no clue why don't you refrain from posting. You always but in and fill my sat night math problem posts with inane garbage. Let someone else who has a clue give the answer.
Well I see you don't think the conduct of a brother is relevant but you do think that every fault of anybody president Obama has ever spoken to IS a reflection on him.
why did you type out that long post and still not even try to solve the problem. It's likely you don't have enough basic skills to even understand the problem. Anybody else wanna take a stab.
I'll give hints if asked.
Andrew was cooking a beef roast in the oven while his neurotic father David was screaming about when it would be done in the background. Andrew was taking meat thermometer temperatures every 20 min because his nerves were on their last leg due to his elderly fathers incessant yelling.
He realized that checking the temp so often made the whole cooking process take longer due to the opening of the oven. He also remembered some math from his college days and decided to estimate the done time of the roast considering the temperature at the meat thermometer in the center of the roast to be a first order system driven by the oven temperature.
Supposing Andrew was correct to model the cooking process as a first order system relating the oven temperature to the meat temperature at the tip of the embedded thermometer, how long will it take for the roast to reach 160F given the initial temperature out of the fridge was 35 deg and the first reading at 50 min cooking time was 80F and the second reading at 100 min cooking time was 116F. How much longer does he have to endure his fathers abuse before the roast is ready for the savage old coot to get his grubby fingers on it as it was cooked to an internal temperature of 160F.