According to Newton\'s Law of Cooling, if a body with temperature T_1 is placed

Question

According to Newton's Law of Cooling, if a body with temperature T_1 is placed in surroundings with temperature T_0 different from that of T_t, the body will either cool or warm to temperature T after t minutes, where T(t)=T_0+(T_1-T_0)e^-kt A chilled jello salad with temperature 42 degree F is taken from a refrigerator and placed in a 68 degree F room. After 15 minutes, the temperature of the salad is 50 degree F. Use Newton's Law of Cooling to find the salad's temperature minutes. After 20 minutes the jello salad will have a temperature of degree F. (Round to the nearest integer.)

Explanation / Answer

T = To +(T1- To)(e^(-kt)

To = 68degF ; T1 = 42 degF ; t= 15 ; T= 50 degF

50 = 68 +( 42-68)e^(-k15)

0.692 = e^(-15k)

taking ln on both sides:

ln(0.692) = -15k

k = 0.0245

Temperature 20 minute:

T =68 +( 42-68)e^(-0.0245*20)

T = 68 - 26*0.61 = 52.14 degF

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