Wednesday

August 20, 2014

August 20, 2014

Posted by **Erica** on Monday, April 25, 2011 at 7:54am.

- calc -
**drwls**, Monday, April 25, 2011 at 8:14amYou are assuming Newton's law of cooling. This leads to a differential equation of T(t) that has a simple exponential decay law. I will skip these steps.

Let k be the cooling rate constant and T' be the surrounding temperature (10 K in this case). t is time in minutes.

The temperature decay equation is

T - T' = 25 e^(-kt)

where the 25 K is the initial temperature difference relative to the surroundings.

Note that dT/dt = -k*(T-T'), as required by the cooling law, and that T(t=0) = 25 + T'

15 = 25*e^(-5k)

-5k = ln(0.6)

k= 0.102 min^-1

When T = 20K,

10 = 25*e^(-0.102 t)

0.4 = e^(-0.102 t)

-.102t = ln(0.4)

t = 9.0 minutes

**Related Questions**

Calculus - Newton's Law of Cooling states that the rate at which an object cools...

math - (TEMPERATURE CHANGE) The rate at which the temperature of an object ...

physics - The average speed of a nitrogen molecule in air is proportional to the...

Chemistry - The SI temperature unit is Celsius? A kelvin is the same temperature...

Physics - An object initially at a temperature of 80 C cools by 1 C in a time of...

Physics(Please help) - An object is inside a room that has a constant ...

Physics - Suppose you are hiking down the Grand Canyon. At the top, the ...

Calculus AB - You pour a cup of coffee. when its poured, it is 130 F above room ...

Chemistry - A gas occupies a volume of 502 cm3 at 20.0 C. What will be its ...

chem - 1. Suppose that a recipe calls for an oven temperature of 189°F. Convert ...