## Thermal Properties of Matter

# Newton's Law of Cooling

- From Newtons law of cooling the rate of loss of heat of a hot body is directly proportional to difference in temperature between the body and its surroundings provided the difference is small. \tt \frac{dQ}{dt}\propto \left(\tau -\tau0\right)
- Newtons law of cooling is applicable if heat lost is mainly due to convection, temperature of every part of body is same.
- As the body cools its rate of cooling goes on decreasing.
- Cooling curve of a hot body is exponential indicating that the temperature decreases exponentially with him.
- Newtons law of cooling is a special case of stefans-Boltzmann's law.

### View the Topic in this video From 42:08 To 55:30

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1. The loss of heat by radiation depends upon the nature of the surface of the body and the area of the exposed surface. We can write -\frac{dQ}{dt}=k\left(T_{2}-T_{1}\right)

2. Rate of loss of heat is given by \tt \frac{dQ}{dt}=ms\frac{dT_{2}}{dt}

3. If a body cools by radiation through a small temperature difference from T_{1} to T_{2} in a short time *t* when the surrounding temperature is T_{0}, then \tt \frac{dT}{dt}=\frac{T_{1}-T_{2}}{t}=k \left[\frac{T_{1}+T_{2}}{2}-T_{0}\right]

4. **Wien's displacement law**: It states that "as temperature of black body *T* increases, the wavelength λ_{m} corresponding to maximum emission decreases" such that \tt \lambda _{m} \propto \frac{1}{T}\ or \ \lambda _{m}T=b

where, b is known as **Wien's constant** and its value is 2.89 × 10^{−3} mK.