In science, Newton’s law of cooling states that the rate of heat loss dQ of a body is proportional to the difference in temperatures between the body and its surroundings, as shown below: [1]

 \frac{d Q}{d t} = h \cdot A(T_{B} - T_{\text{S}})

where h is the (convective) heat transfer coefficient, A is the unit surface area of the body through which the heat is transferred, TB is the temperature of the surface of the body (solid), and TS is the temperature of the surroundings (fluid). [2] Newton’s law of cooling is generally limited to simple cases where the mode of energy transfer is convection, from a solid surface to a surrounding fluid in motion, and where the temperature difference is small, approximately less than 10º C. [3] When the medium into which the hot body is placed varies beyond a simple fluid, such as in the case of a gas, solid, or vacuum, etc., this becomes a residual effect requiring further analysis. [5]

This law of cooling is named after English physicist Isaac Newton who, in the late 17th century, conducted the first experiments on the nature of cooling. Specifically, noting that when the difference in temperature between the two bodies is small, approximately less than 10º C, that the rate of heat loss will be proportional to the temperature difference, Newton applied this principle to estimate the temperature of a red-hot iron ball, by observing the time which it took to cool from a red heat to a known temperature, and comparing this with the time taken to cool through a known range at ordinary temperatures. [3] According to this law, if the excess of the temperature of the body above its surroundings is observed at equal intervals of time, the observed values will form a geometrical progression with a common ratio.

The inaccuracy of Newton’s law become’s considerable at high temperatures. The corrected Newton’s was formulated in 1817 by French physicial chemist Pierre Dulong and physicist Alexis Petit who, experimenting through temperature ranges as high as 243º C, found that the quickness of cooling for a constant excess of temperature, increases in geometrical progression, when the temperature of the surrounding space increases in arithmetical progression. [5]

Human thermodynamics
Iranian-born American engineer Robert Kenoun, in his 2006 book Theory of History and Social Evolution, seems to use an unwritten Joule's second law interpretation of human social systems, in combination with Newton's law of cooling, to argue that evolving human social systems tend towards a minimum of internal energy over time and that conjoined systems will exchange energy during these evolutions, through a process of thermalization or equilibriation, at a rate proportional to their difference in internal energies, in such a manner that greater internal energy (temperature) differences result in greater rates of energy transfer, typified by great violence, such as in war and revolution. [4]

1. Powell, Michael. (2004). Stuff You Should Have Learned at School. New York: Barnes & Noble.
2. Potter, Merle C. and Scott, Elaine P. (2004). Thermal Sciences - an Introduction to Thermodynamics, Fluid Mechanics, and Heat Transfer, (pg. 61). U.S.: Brooks/Cole.
3. Newton’s law of cooling (Heat, section 26), The Encyclopedia Britannica, 1910.
4. Kenoun, Robert. (2006). A Proposition to Theory of History and Social Evolution. Trafford Publishing.
5. Whewell, William. (1866). History of the Inductive Sciences, (section: “Correction of Newton’s law of cooling”, pgs. 149-50). Appleton.

Further reading
‚óŹ Lewis, Michael A. (2010). “The Physics of Inflation: Newton’s Law of Cooling and the Consumer Price Index” (pdf), Journal of Applied Quantitative Methods, 1(5)115-12.

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