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State the Newton's Law of Cooling.
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Answer:
Explanation:
Newton's law of cooling states that the rate of heat loss of a body is directly proportional to the difference in the temperatures between the body and its surroundings. The law is frequently qualified to include provisos that the temperature difference is small and the nature of heat transfer mechanism remains the same. As such, it is equivalent to a statement that the heat transfer coefficient, which mediates between heat losses and temperature differences, is a constant. This condition is generally met in thermal conduction (where it is guaranteed by Fourier's law) as the thermal of most materials is only weakly dependent on temperature, but it is often met only approximately in conditions of convective heat transfer, where several physical processes make effective heat transfer coefficients somewhat dependent on temperature differences. Finally, in the case of heat transfer by thermal radiation, Newton's law of cooling holds only for rather small temperature changes.
Answer:
Newton’s Law of Cooling states that the rate of temperature of the body is proportional to the difference between the temperature of the body and that of the surrounding medium. This statement leads to the classic equation of exponential decline over time which can be applied to many phenomena in science and engineering, including the discharge of a capacitor and the decay in radioactivity.
Newton's Law of Cooling is useful for studying water heating because it can tell us how fast the hot water in pipes cools off. A practical application is that it can tell us how fast a water heater cools down if you turn off the breaker when you go on vacation.
Suppose that a body with initial temperature T1°C, is allowed to cool in air which is maintained at a constant temperature T2°C.
Let the temperature of the body be T°C at time t.
Then by Newton’s Law of Cooling,
(1)
Where k is a positive proportionality constant. Since the temperature of the body is higher than the temperature of the surroundings then T-T2 is positive. Also the temperature of the body is decreasing i.e. it is cooling down and rate of change of temperature is negative.
The constant ‘k’ depends upon the surface properties of the material being cooled.
Initial condition is given by T=T1 at t=0
Solving (1)
(2)
Applying initial conditions;
Substituting the value of C in equation (2) gives
This equation represents Newton’s law of cooling.
If k <0, lim t --> ∞, e-kt = 0 and T= T2 ,
Or we can say that the temperature of the body approaches that of its surroundings as time goes.
The graph drawn between the temperature of the body and time is known as cooling curve. The slope of the tangent to the curve at any point gives the rate of fall of temperature.
In general,
where,
T(t) = Temperature at time t,
TA = Ambient temperature (temp of surroundings),
TH = Temperature of hot object at time 0,
k = positive constant and
t = time.
Example of Newton's Law of Cooling:
This kind of cooling data can be measured and plotted and the results can be used to compute the unknown parameter k. The parameter can sometimes also be derived mathematically.