Question

From Newton's law of cooling, show that log, (T-T.) = - kt +C
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Answer 1

Answer:

Newton’s law of cooling describes the rate at which an exposed body changes temperature through radiation which is approximately proportional to the difference between the object’s temperature and its surroundings, provided the difference is small.

Definition: 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.

Solved ExamplNewton’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.

Newton’s Law of Cooling Formula

Greater the difference in temperature between the system and surrounding, more rapidly the heat is transferred i.e. more rapidly the body temperature of body changes. Newton’s law of cooling formula is expressed by,

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.