Derive Newton's law of cooling from Stefan-Boltzman law. - Vidyadip

Question

Derive Newton's law of cooling from Stefan-Boltzman law.

✓

Answer

For a non-black body at temperature T surrounded by an enclosure $T_0$ (where $T > T_0$), we have $\text{E}=\text{e}\sigma(\text{T}^4-\text{T}^4_0)$ where e is a constant, and its value depends upon the physical nature of the emitting surface.
$\therefore\text{E}=\text{e}\sigma(\text{T}^2+\text{T}^2_0)(\text{T}^2-\text{T}_0^2)$ $=\text{e}\sigma(\text{T}^2+\text{T}^2_0)(\text{T}+\text{T}_0)(\text{T}-\text{T}_0)$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Thermal Properties of Matter→Thermal Properties of Matter — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

A student records the initial length l, change in temperature $\Delta\text{T}$ and change in length $\Delta\text{l}$ of a rod as follows:

S.NO.	l(m)	$\Delta\text{T(C)}$	$\Delta\text{l}(\text{m})$
$1.$	$2	$10	$4 \times 10^{-4}$
$2.	$1	$10	$4 \times 10^{-4}$
$3.	$2	$20	$2 \times 10^{-4}$
$4.	$3	$10	$6 \times 10^{-4}$

If the first observation is correct, what can you say about observations 2, 3 and 4.

Water falling from a $50m$ high fall is to be used for generating electric energy. If $1.8 x 10^5kg$ of water falls per hour and half the gravitational potential energy can be converted into electric energy, how many $100W$ lamps can be lit?

A straight wire carrying an electric current is placed along the axis of a uniformly charged ring. Will there be a magnetic force on the wire if the ring starts rotating about the wire? If yes, in which direction?

In a glass capillary tube, water rises upto a height of 10.0 cm while mercury fall down by 5.0 cm in the same capillary. If the angles of contact for mercury glass is $60^{\circ}$ and water glass is $0^{\circ}$, then find the ratio of surface tension of mercury and water.

An object is thrown vertically upward with some speed. It crosses two points $p$ and $q$ which are separated by $h$ metre. If $t_p$ is the time between $p$ and the highest point and coming back and $t_q$ is the time between $q$ and the highest point and coming back, relate acceleration due to gravity, $\mathrm{t}_{\mathrm{p}}, \mathrm{t}_{\mathrm{q}}$, and h .

Let $\overrightarrow{\text{A}}$ and $\overrightarrow{\text{B}}$ be the two vectors of magnitude 10 unit each. If they are inclined to the X-axis at angles 30° and 60° respectively, find the resultant.

A hospital uses an ultrasonic scanner to locate tumours in a tissue. What is the wavelength of sound in the tissue in which the speed of sound is $1.7km s^{–1}$? The operating frequency of the scanner is $4.2$ MHz.

QUESIION The distance between earth and moon is $3.8 \times 10^5 km$ and the mass of earth is 81 times the mass of moon. Deduce the position of a point on the line joining the centres of earth and moon, where the gravitational field is zero. What would be the value of gravitational field there due to earth and moon separately?

A body of mass 2 kg is being dragged with a uniform velocity of $2 \mathrm{~ms}^{-1}$ on a rough horizontal plane. The coefficient of friction between the body and the surface is 0.2 . Calculate the amount of heat generated per second.
Take $\mathrm{g}=9.8 \mathrm{~ms}^{-2}$ and $\mathrm{J}=4.2 \mathrm{~J} / \mathrm{cal}^{-1}$.

Two small bodies of masses $10kg$ and $20kg$ are kept a distance $1.0m$ apart and released, Assuming that only mutual gravitational forces are acting, find the speeds of the particles when the separation decreases to $0.5m$.