Mr. A and Mr. Z were both given a cup of tea. Mr. A added a spoonful of cream and then waited for 10 minutes before drinking the tea. Mr. Z waited for 10 minutes first, then added a spoonful of cream, then drank it. Who drank the hotter tea?
We will make the assumption that when an amount of liquid with mass m and temp. T1 is mixed with the liquid of mass M of temperature T2, will have the temperature: (mT1+MT2)/(m+M)
(You can ignore this part if it's not correct, but here is what i did so far):
If we first ignore the cream: Let T(t)= The tea's temperature and R= The room temp. (constant)
So the differential equation is: dT/dt= -k(T-R), and separating the variables and solving I got:
T(t)=R+(To-R)*e^(-kt), where To= T(0), and To= (R+C) and C=(To-R), if you're wondering on what I did with the constant after i integrated.
Then for my 2nd and 3rd step i was going to try to find the temperature of the tea for both Mr. A and Mr. Z to see who had the hotter tea, but not sure how to do that exactly...?
And once again, if this is wrong, you can ignore it.
We will make the assumption that when an amount of liquid with mass m and temp. T1 is mixed with the liquid of mass M of temperature T2, will have the temperature: (mT1+MT2)/(m+M)
(You can ignore this part if it's not correct, but here is what i did so far):
If we first ignore the cream: Let T(t)= The tea's temperature and R= The room temp. (constant)
So the differential equation is: dT/dt= -k(T-R), and separating the variables and solving I got:
T(t)=R+(To-R)*e^(-kt), where To= T(0), and To= (R+C) and C=(To-R), if you're wondering on what I did with the constant after i integrated.
Then for my 2nd and 3rd step i was going to try to find the temperature of the tea for both Mr. A and Mr. Z to see who had the hotter tea, but not sure how to do that exactly...?
And once again, if this is wrong, you can ignore it.