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Question
Answer the following question.
State Newton’s law of cooling and explain how it can be experimentally verified.
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Solution
The rate of loss of heat dT/dt of the body is directly proportional to the difference of temperature (T - T0) of the body and the surroundings provided the difference in temperatures is small.
Mathematically, Newton’s law of cooling can be expressed as:
`"dT"/"dt" prop ("T" - "T"_0)`
∴ `"dT"/"dt" = "C"("T" - "T"_0)`
where, C is constant of proportionality.
Experimental verification of Newton’s law of cooling:
- Fill a calorimeter upto `2/3` of its capacity with boiling water. Cover it with a lid with a hole for passing the thermometer.
- Insert the thermometer through the hole and adjust it so that the bulb of the thermometer is fully immersed in hot water.
- Keep calorimeter vessel in constant temperature enclosure or just in open air since room temperature will not change much during the experiment.
- Note down the temperature (T) on the thermometer at every one-minute interval until the temperature of water decreases by about 25 °C.
- Plot a graph of temperature (T) on the Y-axis against time (t) on the X-axis. This graph is called the cooling curve as shown in the following figure.
Cooling curve - Draw tangents to the curve at suitable points on the curve. The slope of each tangent is `lim_(Delta"t" -> 0) (Delta "T")/(Delta "t")` and gives the rate of fall of temperature at that temperature (T).
- Now the graph of `|"dT"/"dt"|` on Y-axis against (T - T0) on X-axis is plotted with (0,0) origin. The graph is a straight line and passes through origin as shown in the following figure, which verifies Newton’s law of cooling.
Graphical verification of Newton’s law of cooling
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