Compare the temperatures of your cup of coffee at time t a) if you add cream and

Question

Compare the temperatures of your cup of coffee at time t

a) if you add cream and let the mixture cool;

b) if you let the coffee and cream sit on the table and mix them at time t

Hints: Assume Newton's law of cooling for both coffee and cream (where it is a law of heating). Combine n' units of cream initially at temperature T0' with n units of coffee initially at temperature T0, and find the temperature at time t in a) and b) assuming that the air temperature remains a constant Ta, and that the proportionality constant in the law of cooling is the same for both coffee and cream.

Explanation / Answer

Note : question wasn't not clearly ,        The fallowing equation ,may be helful to u By the Newton's law of cooling we have , Rate of cooling : dT/dt = k(T - Ta) ,           (differential equation) K is the Thermal conductivity where air temperature remains a constant Ta
dT / (T - Ta) = k dt
ln(T - Ta) = kt + c
T = ce(kt) + Ta
T = (To - Ta) e(kt) + Ta

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