It is in relation to newtons law of cooling and I have to fill in a chart where t is time in seconds, T(t) is the temp of the object
and Ta is the ambient temp
t=0 T(t)= 96.41 Ta= 26.1
I have to fill in the rest which is
T(t) - Ta
which would = 70.31
ln(T(t) - Ta)
which would = aprox 4.253
but then it asked for
delta T(t)
I don't know what to do here, I know delta generaly refers to the difference of something but Im stumped by this one.
2007-07-18 07:55:26 · 7 answers · asked by miss_kitty_1984 2 in Science & Mathematics ➔ Mathematics
Delta T(t) means the change in temperature over/with repsect to time. I would assume from the starting temp to the end temp.
2007-07-18 07:57:27 · answer #1 · answered by Lady Geologist 7 · 0⤊ 0⤋
T(t) = Ta +(To-Ta)e^-kt, where:
To = 96.41 degrees = initial tempearture
Ta = ambient temperature
k is a constant to be determined
T(t) = temperature at any time t
So T(t) = 26.1 + (96.41-26.1)e^-kt
T(t) = 26.1 + 70.31e^-kt
k = ln(T(t) -Ta)/(-70.31t)
So to find k, you need to know T(t) at some time t different from 0. They must have told you that info.
In any event, once you have k , you can find dT/dt which is what I think they ar calling delta t. If not , then delata T simply indicates the change in temperature between time t=0 and time t, which you have not been given.
T
2007-07-18 16:05:24 · answer #2 · answered by ironduke8159 7 · 0⤊ 0⤋
You are correct that delta refers to change. In this case, it would probably be the change from the initial temperature. So delta T(t) is probably T(t) - T(0).
2007-07-18 14:57:51 · answer #3 · answered by DavidK93 7 · 0⤊ 0⤋
any delta is a change.
delta (T) where capital T is conventionally used for Temperature simply means the change in temperature.
Delta T (t) : small t conventionally equals time would just be the average rate of change is temperature vs time.
take total delta (T) and divide by the elapsed time (in seconds) and you've got it.
2007-07-18 15:06:16 · answer #4 · answered by Anonymous · 0⤊ 0⤋
If you have only this one set of figures, then I am baffled.
However, if you have two values t[1] and t[2] of t (close together) and corresponding values T(t[1]) and T(t[2]), I would interpret delta(T(t)) to mean T(t[2]) - T(t[1]).
2007-07-18 15:02:55 · answer #5 · answered by Anonymous · 0⤊ 0⤋
delta T would be the change in temperature
2007-07-18 14:58:01 · answer #6 · answered by Anonymous · 0⤊ 0⤋
delta = difference
so if delta T(t) is asked, then the answer is T (t)- T(a) = ...
2007-07-18 15:00:01 · answer #7 · answered by Blue Moon 3 · 0⤊ 0⤋