Question

According to the Newton's law of cooling, rate of loss of the heat is directly proportional to the-
1. Temperature of the body only
2. Temperature of the surrounding only
3. Temperature difference between the body and the surrounding.
4. None of the above
5.

Answer 1

Correct Answer - Option 3 : Temperature difference between the body and the surrounding.

CONCEPT:

• Newton's Law of Cooling: It states that the rate of cooling or rate of loss of heat is directly proportional to the difference between the temperature of the body and temperature of the surrounding medium, Nature, and extent of the exposed surface.
  • The rate of cooling of water decreases with a fall in temperature.

EXPLANATION: 

• Newton's law of cooling states that rate of cooling or rate of loss of heat is directly proportional to-
  • the temperature difference between the body and the surrounding.

• Let consider a hot body at temperature T and temperature of the surrounding be T₀, so according to Newton's Law of Cooling we can say that 
• Rate of loss of heat ∝ Temperature difference between the body and surrounding,
• which can be written as these three formulae, where (T is the temperature of the body, T₀ is the temperature of its surrounding, K is proportionally constant, c is constant of integration and e is exponential value)

\(log_e (T-T_0)= -Kt+c\)

\( (T-T_0)= e^{-Kt+c}\)

\( T= T_0 + e^ce^{-Kt}\)