Solution:

For any given temperature and wavelength, the ratio of the emissive power to the absorptive power is the same for all substances and is equal to the emissive power of a perfectly black body at the same temperature.

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Solution:

According to Wien's law, the wavelength `gamma_m` for which the emittance of a black body is maximum, is inversely proportional to its absolute temperature. '`gamma_m,T` = constant. This constant is written as b and has a value of `0.288 cmK` in the CGS units and `2.88 xx l0^(-3) ` mK in the S.I. units.

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Solution:

According to Wien's law, the product of the wavelength corresponding to maximum intense radiation and the absolute temperature is a constant, i.e., `gamma_mT =` constant.

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Solution:

Conduction, Convection and Radiation are the three modes of transference of heat. Conduction. Transfer of heat by the collision among the molecules with their neighbours is called conduction. Rate of heat transfer is given by,

`Q/t = (KAdtheta)/(dl)` where K is called thermal conductivity

Convection. is the heat transfer mode in which the molecules shift themselves from place to place to transfer heat. Radiation. is the fastest mode of heat transfer which does not require any medium. In thermos flask conductors, conduction of heat is avoided. By having an evacuated region between two walls, the convection of heat is avoided. By having reflecting smooth and polished wall, the energy trying to move outward from the hot substance is reflected back and so outward radiation is avoided.

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Solution:

Conduction. Transfer of heat by the collision among the molecules with their neighbours is called conduction. Rate of heat transfer is given by,

`Q/t = (KAdtheta)/(dl)`

where K is called thermal conductivity.
Thermal conductivity is defined as heat energy transferred in unit time from unit area having a difference in temperature of unity over unit length. It is expressed in

`J S^(-1) M^(-1) o_C or W m^(-1) K^(-1)`

When rods are arranged in series, Q/t is same in both and the sum of the difference in temperature across their ends is the difference at the open ends.

`i.e., (theta_1 - theta) + (theta- theta_2) = (theta_1 - theta_2)`

Using `Q/t = (dtheta)/(R_(Nth)` we get

`(Q/t) R_1 + (Q/t)R_2 = (Q/t)R_(Nth)`

:. Net resistance `= R_(lth) + R_(2th)` When rods are arranged in parallel and the difference in temperature will be the same, then

`(Q/t)_N = (Q/t)_1 + (Q/t)_2`


i.e `(dtheta)/(R_N) = (dtheta)/(R_1)+ (Dtheta)/(R_2)`

`=> 1/(R_N) = 1/(R_1) + 1/(R_2)`

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Solution:

`"Black body."` A perfectly black body is that which absorbs completely the radiations of all wavelengths incident on it. As a perfectly black body neither reflects nor transmits any radiation, therefore the absorbtance or absorbing power of a perfectly black body is unity. We know that the colour of an opaque body is the colour (i.e., wavelength) of radiation reflected by it. As a black body reflects no wavelength, it appears black whatever be the colour of radiation incident on it. When a perfectly black body is heated to a suitable high temperature, it emits radiations of all possible wavelengths. The radiations given out by a perfectly black body are called plain body radiations or full radiations or total radiations. A perfectly black body cannot be realised in practice. Fery designed a perfectly black body which is most commonly used. It consists of a hollow double walled metallic sphere having a narrow opening 0 on the side and a conical projection P inside just opposite to it. The inside of the sphere is coated with lamp black. Any radiation entering the sphere through the opening 0 suffers multiple reflections at its inner walls and about 97% of it is absorbed by lamp black at each reflection. Therefore, after a few reflections, almost entire radiation is absorbed. The projection helps in avoiding any direct reflection which even otherwise is hardly possible because of the small size of the opening 0. When this body is placed in a bath at fixed temperature, the heat radiations come out of the hole. The opening thus acts as a black body radiator. It should be remembered that only the opening (and not the walls) acts as a black body radiator. Energy distribution in black body.

(i) At a given temperature with increase in wavelength, the energy radiated increases and then decreases.
(ii) As the temperature increases, there is a shift in the wavelength towards lesser values corresponding to maximum intense wavelength, as given by

`gamma_m T = constant (2.89 xx10^(-3)mK)`

(iii) Area below the graph in a specified wavelength range is a measure of the radiant energy in that wavelength range.

Wein's law and its application. According to Wien's law, the product of the wavelength corresponding to maximum intense radiation and the absolute temperature is a constant

i.e., `gamma_m T=` constant.

To find the temperature of stars, one can use Wien's law. If the wavelength of maximum intense component is known, temperature can be found from `gamma_m T = b = 2.89 xx 10^(-3) Mk`

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Solution:

Thermal conductivity is defined as heat energy transferred in unit time from unit area having a difference in temperature of unity over unit length. It is expressed in

`Js^(-1) m^(-1) o^C or Wm^(-1) K^(-1)`
It is given by

`K = (Q/t). (dl)/(Adtheta)`

and is expressed in S.I. system

as `text(joule)/text(sec) text(metre)/text(metre)^2K i.e Js^(-1) M^(-1) K^(-1)`

or `Wm^(-1) K^(-1)`

`A = 1000 cm^(-2) = 10^(-1) m^2`

`l = 0.4 xx 10^2 m`

`dtheta = 37 - (-5) = 42 o_C`

`K = 2.2 xx 10^(-3) xx 4.2 xx 10^(+2) Js^(-1) m^(-1) K^(-1)`

`Q/t = K (Adtheta)/(l)`

`= ((2.2xx10^9-3) xx 4.2 xx 10^2 xx 10^(-1) xx 42)/(0.4xx10^9-2)`

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Solution:

Emissive Power. The amount of energy radiated per second per unit area of a hot body is called emissive power (e). Absorptive Power. The amount of energy absorbed per second per unit area out of the energy incident normally is called absorptive power (a). The ratio of emissive to absorptive power of all bodies at the same temperature is a constant and is equal to the emissive power of a hot black body at the same temperature.

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Solution:

It is the temperature at which the three phases of water, namely, ice, liquid water and water vapours are equally stable and coexistent. The triple point is suitable because it is unique, i.e., it occurs at one single temperature `= 273.16K` and one single pressure of about `0.46 cm` of the Hg column.

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