You place a cup of 205oF coffee on a table in a room that is 72oF, and 10 minutes later, it is 195oF. Approximately how long will it be before the coffee is 180oF? Use Newton's law of cooling: $$T(t)=T _{A}+(T _{o}-T _{A})e ^{-kt}$$

A. 15 minutes
B. 25 minutes
C. 1 hour
D. 45 minutes

Question

You place a cup of 205oF coffee on a table in a room that is 72oF, and 10 minutes later, it is 195oF. Approximately how long will it be before the coffee is 180oF? Use Newton's law of cooling: $$T(t)=T _{A}+(T _{o}-T _{A})e ^{-kt}$$

A. 15 minutes
B. 25 minutes
C. 1 hour
D. 45 minutes

anonymous · Answer

Ta = 72
To=205

anonymous · Answer

use the same rule as before

anonymous · Answer

make sure you can use degrees F in this equation.  i think u might have to convert to kelvin

anonymous · Answer

how would i do that?? :o

anonymous · Answer

i dont know if you have to do that or not, its been a long time since i have taken heat transfer

anonymous · Answer

hm, so just to clarify what I am doing, would i do ln(72/205) ?

anonymous · Answer

first you need to find k

anonymous · Answer

how do i do that?

anonymous · Answer

so you have

195 = 72 + (205-72)*e^(-k*10)

anonymous · Answer

(195-72)/(205-72) = e^(k*10)

anonymous · Answer

so take the ln of both sides, you get

ln((195-72)/(205-72)) = k*10

solve for k

anonymous · Answer

then once you know k, u perform the same operation to find t for the second case, which is cooling down to 180 instead of 195