Heat Transfer

02 - Time for the thermometer reading to drop to within half degree of the air temperature

Problem 02
A thermometer reading 75 degree Fahrenheit is taken out where the temperature is 20 degree Fahrenheit. The thermometer reading is 30 degree Fahrenheit 4 minutes later. Find the time (in minutes) taken for the reading to drop from 75 degree Fahrenheit to within half degree of the air temperature.

01 - Thermometer reading after 6 minutes of being outside

Problem 01
A thermometer which has been at the reading of 70°F inside a house is placed outside where the air temperature is 10°F. Three minutes later it is found that the thermometer reading is 25°F. Find the thermometer reading after 6 minutes.

Newton's Law of Cooling

Newton's Law of Cooling states that the temperature of a body changes at a rate proportional to the difference in temperature between its own temperature and the temperature of its surroundings.

We can therefore write

$\dfrac{dT}{dt} = -k(T - T_s)$

T = temperature of the body at any time, t
Ts = temperature of the surroundings (also called ambient temperature)
To = initial temperature of the body
k = constant of proportionality

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