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_1 the body will either cool or warm to temperature T(t) after t minutes, where T(t) = T_0 + (T_1 - T_0)e^-kt. A cup of coffee with temperature 130 degree F is placed in a freezer with temperature 0 degree F. After 5 minutes, the temperature of the coffee is 87 degree F. Use Newton's Law of Cooling to find the coffee's temperature after 10 minutes. After 10 minutes the coffee will have a temperature of degree F. (Round to the nearest integer.)

Explanation / Answer

first of all using given parameters we have to calculate k

87=0+(130-0)e-5k

e5k=130/87

e5k=1.494

ln(e5k)=ln(1.494)

5k=0.4015

k=0.083

after 10 minutes temperature will be

T=0+(130-0)e-10(0.083)

T=0+130e-0.83

T=130(0.436050)

T=56.69 F

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