Question

Suppose a bottle of wine at a room temperature of 72 degree fahrenheit is place in a refrigerator at 40 degree fahrenheit to cool before a dinner party. After an hour the temperature of the wine is found to be 61.5 degree fahrenheit. Find the constant k, to two decimal places, and the time, to one decimal place it will take the wine to cool from 72 to 50 degree fahrenheit

Answer 1

\[ T=T_{m}+(T_{0}-T_m)e^-kt\]

Answer 2

that is the equation

Answer 3

e is raise to -kt

Answer 4

T=Tm+(To-Tm)=e^-kt
61.5=40 +(72-40)e^-k(1hour)
(61.5-40)=(72-40)e^-k(1hour)
(61.5-40)/(72-40)=e^-k(1hour)
21.5/32 =e^-k(1) taking ln on both sides gives
ln(21.5/32)= -k
-0.40=-k
k=0.40
now
50=40+(72-40)e^-0.4t
50-40=(72-40)e^-0.4t
10=32e^-0.4t
10/32=e^-0.4t taking ln on both sides
ln(10/32)=-0.40t
t= -ln(10/32)/0.40
t=2.9 hours ...ans

Answer 5

if you have any question let me know

Answer 6

is everything ok? any question xiongvue?