define newton's law of cooling
Answers
Newton’s Law of Cooling
Named after the famous English Physicist, Sir Isaac Newton, Newton’s Law of Cooling states that the rate of heat lost by a body is directly proportional to the temperature difference between the body and its surrounding areas. Given that such difference in temperature is small and the nature of the surface radiating heat remains constant. To put it in simpler terms, we may say that the hotter an object is, the quicker it cools down.
By temperature difference, we mean that any phenomenon which leads to the flow of energy into a system or flow of energy from any system into the surrounding area. In the former case, the object heats up, whereas in the latter, the object cools down. Newton’s Law of Cooling leads to the often cited equation of exponential decline over time.
This can be applied to several phenomena of science and engineering which includes discharge of a capacitor and the decay in radioactivity. The law is helpful in the study of heating water as it can help us calculate what speed the heater in the pipes cools off. To understand the application of this law in a practical sense would be that if you are going on a vacation and turn off the breaker, it will be able to tell you how fast the water heater will cool down.
Calculating the Rate of Heat Transfer
When we apply the definition of Newton’s Law of Cooling to an equation, we can get a formula. So, as per the law, the rate of a body cooling is in direct proportion to the difference in body’s temperature. Therefore,
We take body temperature as T and the surrounding temperature as T0
The difference in temperature stays constant at 300 C. Calculating the thermal energy Q.
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According to Newton’s law of cooling, the rate of loss of heat from a body is directly proportional to the difference in the temperature of the body and its surroundings.
Newton’s law of cooling is given by, dT/dt = k(Tt – Ts)
Where,
Tt = temperature at time t and
Ts = temperature of the surrounding,
k = Positive constant that depends on the area and nature of the surface of the body under consideration.
Formula:-
T(t) = Ts + (To – Ts) e-kt
Where,
t = time,
T(t) = temperature of the given body at time t,
Ts = surrounding temperature,
To = initial temperature of the body,
k = constant
Limitations of Newtons Law of Cooling:-
-The difference in temperature between the body and surroundings must be small,
-The loss of heat from the body should be by radiation only,
-The major limitation of Newton’s law of cooling is that the temperature of surroundings must remain constant during the cooling of the body.
Methods to Apply Newton’s Law of Cooling
Sometime when we need only approximate values from Newton’s law, we can assume a constant rate of cooling, which is equal to the rate of cooling corresponding to the average temperature of the body during the interval.
i.e.
dθ\dt = k(<q> – q0) . . . . . . . (4)
If qi and qf be the initial and final temperature of the body then,
<q> = (qi + qf)/2 . . . . . (5)
Remember equation (5) is only an approximation and equation (1) must be used for exact values.