Login

Articles

Newton’s law of cooling

Print

Introduction to Newton’s law of cooling

Newton’s law of cooling states that a body’s rate of loss of heat is directly proportional to the temperature difference between the body and its surroundings. When a hot body is placed at a lower temperature, the hot body slowly cools down by losing heat energy to its surroundings.

Isaac Newton found that the temperature of a hot object decreases at a rate proportional to the difference between it and the surrounding temperature. Obversely, an object colder than its surroundings warms at a rate proportional to the same difference.


Equation of Newton’s law of Cooling

The formula governing the law is dQ/dt = c (T - S)        (1)

where T is the object's temperature, S is the surrounding temperature, dQ is the quantity of heat lost in time dt, and c is a constant of proportionality.



Derivation of Equation

For a small temperature difference between a body and its surroundings, the body’s rate of cooling is directly proportional to the temperature difference. If a body of temperature T and surface area A is kept in a surrounding temperature T0(T0 < T), then net loss of thermal energy per unit time amounts to:


dQ/dt =εσ A(T0 - T00)


If the temperature difference is small, then:


     T = T0 + ΔT


=>εσ A[(T0 +Δ T)4] =εσ A[T04 (1 + ΔT/T0 )4 - T04]


=>εσ AT04[1 + 4 ΔT/T0 + higher powers of ΔT/T - 1]


= 4εσ AT03 ΔT


Now, the rate of loss of heat at temperature T is:


dQ/dt = -mc dT/dt

mc dT/dt = - 4εσ AT03[T - T0]


dT/dt = - K[T - T0]


K = 4εσAT03 /mc

dT/dt  α(T - T0)


We know that the heat that a body loses depends on its heat capacity. If m is the mass of the body and s is the specific heat, then


                                     dQ/dt = m s dT/dt


With Newton’s law (eq. 1), this equation can be used to find the specific heat capacity of the liquid.

 

                                                                            ***


Want to know more about Newton’s law of cooling? Click here to schedule a live session with an eAge eTutor!



About eAge Tutoring:

eAgeTutor.com is the premium online tutoring provider.  Using materials developed by highly qualified educators and leading content developers, a team of top-notch software experts, and a group of passionate educators, eAgeTutor works to ensure the success and satisfaction of all of its students.

Contact us today to learn more about our guaranteed results and discuss how we can help make the dreams of the student in your life come true!


Reference links:

    

Archives

Blog Subscription