According to newtons law of cooling, the temerature of the body and the temperature of the surrounding medium
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Step 1: Understand Newton's Law of Cooling, which states that the rate of change of the temperature of an object is proportional to the difference between its temperature and the ambient temperature of its surroundings. Show more…
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Newton’s law of cooling, holds good only if the temperature difference between the body and the surroundings is?
Kamlesh G.
According to Newton's law of cooling, the temperature of a body changes at a rate proportional to the difference between the temperature of the body and the temperature of the surrounding medium. Thus, if Tm is the temperature of the medium and T = T(t) is the temperature of the body at time t, then T' = -k(T - Tm) where k is a positive constant. In this exercise, you will verify that T = Tm + (To - Tm)e^-kt is a solution to the differential equation. Here To denotes the initial temperature T(0) of the body. (a) First substitute the above expression for T into the left side of the differential equation. In other words, compute T'. (b) Next substitute the above expression for T into the right side of the differential equation. In other words, compute -k(T - Tm).
Sri K.
Newton's law of cooling states that the rate of change of temperature of an object is proportional to the difference in temperature between the object and the surrounding medium. Thus, if $T$ is the temperature of the object after $t$ hours and $T_{M}$ is the (constant) temperature of the surrounding medium, then $$\frac{d T}{d t}=-k\left(T-T_{M}\right)$$ where $k$ is a constant. Use this equation. According to the solution of the differential equation for Newton’s law of cooling, what happens to the temperature of an object after it has been in a surrounding medium with constant temperature for a long period of time? How well does this agree with reality?
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