Question

T(t) = T0 + (T1 − T0) · 2^(−t/τ) [in celsius]

Answer 1

where T is the temperature of the coffee at the time t (in minutes), the room temperature T0, T1 coffee starting temperature
and τ a constant dependent on the cup warmth.
1). Plot the relationship graphically.
2). Show that τ is the time it takes for the difference between the coffee and the room's temperature to be half of the temperatur
3) .Charlotte has just poured a cup of freshly brewed coffee but due to an unforeseen event she is not able to drink coffee until after t0 min. Charlotte wants his coffee mixed with p% the refrigerator milk temperature T2 <T0. She is interested in making the coffee is as warm as possible when she drinks it. When is it best to put the milk immediately after pouring, or just before she drinks coffee? Indicate the difference between the final temperatures return for the two variants. You can assume that τ has the same value for pure coffee for coffee contaminated with milk.

Answer 2

I need help with 1 and 3, I think 2 is just like this:
\[T _{(\tau)}=T _{0}+(T _{1}-T _{0})*2^{\frac{ -\tau }{ \tau }} = T _{(\tau)}=T _{0}+(T _{1}-T _{0})*\frac{ 1 }{ 2^{1} }=\frac{ T _{(\tau)}=T _{0}+(T _{1}-T _{0}) }{ 2 }\]

Answer 3

I mean it equals this

\[=T _{(\tau)}=T _{0}+\frac{ (T _{1}-T _{0}) }{ 2 }\]

Answer 4

@freckles what you thinking`?

Answer 5

I'm reading up on Newton's law of cooling...

Answer 6

\[T_t=T_0+(T_1-T_0)2^{\frac{-t}{\tau}} \\ T_t \text{ temperature of object at time } t \\ T_0 \text{room temp } \\ T_1 \text{ initial temperature of heated object } \\ \\ \text{ so if the milk goes in at coffee pouring time then the} \\ \text{ initial temperature of the coffee will be different } \\ \text{ so } T_1 \text{ will now be replaced with } T_1-\Delta T \\ T_t'=T_0+(T_1- \Delta T-T_0)2^{\frac{-t}{\tau}} \\ \text{ but if the milk goes in right before she drinks it } \\ \text{ is a change to the final temperature } \\ \text{ instead of the beginning temperature } \\ \text{ so in this case it would be } \\ T_t=T_0+(T_1-T_0)2^\frac{-t}{\tau} -\Delta T\]

Answer 7

There we go now just compare T' and T to find which is bigger.

Answer 8

See if T'-T>0 or if T'-T<0
If T'-T>0 then T'>T
and
If T'-T<0 then T'<T