HL Maths problem

nailforhammer

Can't think how to answer question 8 of EDCO papers p123 part (c)
If anyone could help me I would be very grateful.


Background:
The rate at which the surface of an object cools depends on the temp difference between the object and the temperature of the surrounding environment.

This is known as newton's law of cooling and is represented by
T(t) = Ts + (To - Ts) e^-kt (the arrow means to the power of)

T(t) is the temp at time t
Ts is the surrounding temp
To is the initial temp of the object
k is a constant

John makes coffee at 100°C and pours it into a cup. The temperature of these surrounding air is 20°C.

From doing part (a) k is equal to 0.127446

Question C:
When John is about to add milk to the coffee the phone rings.
Should he pour milk into the coffee first or answer the phone and then add the milk?
He likes his coffee as hot as possible. In either case he uses the same amount of milk.

robman60

What you must do is make up your own figure using common sense for how many degrees the milk will lower the temperature by. This will be constant as the question explicitly states that the same amount of milk was added both times. I think I said 15C or something like that. It doesn't matter as long as you use the same for both. Then plug the numbers into the formula taking initial temperature as 100 and then subtracting the 15C at the end and then do the same except take initial temp. as 100-15 and see which gives the higher number.

I don't have my papers home with me but I remember it will stay warmer if you add the milk prior to answering the phone call. The reason being it loses heat more rapidly the hotter it is.

Of course, by the time you've worked it out your coffee will be cold and your friend will have hung up. :pac:

nailforhammer

robman60 wrote: »

What you must do is make up your own figure using common sense for how many degrees the milk will lower the temperature by. This will be constant as the question explicitly states that the same amount of milk was added both times. I think I said 15C or something like that. It doesn't matter as long as you use the same for both. Then plug the numbers into the formula taking initial temperature as 100 and then subtracting the 15C at the end and then do the same except take initial temp. as 100-15 and see which gives the higher number.

I don't have my papers home with me but I remember it will stay warmer if you add the milk prior to answering the phone call. The reason being it loses heat more rapidly the hotter it is.

Of course, by the time you've worked it out your coffee will be cold and your friend will have hung up. :pac:

Yeah that's a good point tbh I mean just pour the milk in and drink the coffee while you talk on the phone... God! Hahaha