Heat Conduction

In this mechanism, heat transfer is due to vibration amplitudes of molecules & atoms present in solids.

Consider a cubicle of solid. Let us maintain one face of cube at high temperature (TH) and other opposite face at low temperature(Tc).

Due to temperature difference an amount of heat energy (Q) passes from  hot face to cold face in time 't'.

Conduction rate  Pcond (amount of energy transferred for uni time) is

Pcond = Q/t = K*A*(TH-Tc)/d;

where 'K' is coefficient of thermal conductivity, a constant for given material.
           'd' is thickness of slab
           'A' Area of slab
            't' is time of conduction

Therefore, Q= K*A(TH-Tc)*t/d

Note: i) 'K' depend on nature of material of which slab is made
         ii) A good thermal conductor has 'K' greater value.

Thermal Resistance to conduction(R-value):

This explains resisting of thermal conductivity. The R-value(thermal resistance) of a slab of thickness 'd' is defined as R=d/k. Thus material having less value of 'K' will have higher R-value and thus acts as a good thermal insulator.

Note:

i) 'R' is properly assigned to specified thickness of slab but not to material of slab.
ii) In steady state, conducting rates thru any no. of materials must be equal.
     Therefore, Pcond = A*(TH-Tc) / Σ(d/K)
iii) Heat is transferred from molecule to molecule by conduction. In this case molecules do not bodily move but simply vibrate.

Black body and its Radiation

A perfectly black body is the one which absorbs all the radiations of all wavelengths incident on it. Since it neither reflects not transmits any radiation it appears black in color what may be the color of incident radiation.

According to Kirchoffs law, a body which is capable of absorbing radiation must also be capable of emitting all possible wavelengths. So a perfectly black body is a good absorber as well as good radiator. When it is heated to a suitable high temperature, it emits radiations of all wavelengths (continuous spectrum). As the radiations emitted by black body is rich in maximum possible wavelengths and hence such Radiations are known as full Radiation or Total Radiation.     

The wavelength of emitted Radiation by a black body depends only on its temperature and is independent of the material of the body.

There is no body acting as perfect black body. The nearest approach is lamp black or platinum black. These are capable of absorbing the visible and a part near infrared but far infrared (heat Radiation) are reflected. So perfectly black body is just an ideal concept. For all practical purposes a lamp blacked surface can be considered as perfectly black body.

Energy Distribution in Black body Radiation

The distribution of energy in black body radiation for different wavelengths and at various temperatures was determined experimentally by Lummer and Pringsheim in 1899. They used the black body as an electrically heated chamber with narrow aperture.

The temperature of heated enclosure is measured by thermocouple.

The parallel beam of Radiation is allowed to incident on a "fluorspar prism" instead of a glass prism. The reason behind not using glass prism is that it absorbs some heat radaition.

The radiation is detected by means of Bolometer. Bolometer is an instrument to detect Thermal Radiation. The Bolometer is a linear type due to Lummer and Kurlabaum and is fitted with galvanometer 'G'. The deflection produced in the Galvanometer gives the intensity of Radiation, Eƛ. This is defined such that quantity Eƛ.dEƛ is the energy, for wavelengths lying between ƛ and ƛ+dƛ emitted per second per unit surface area of black body.   

The wavelengths at different parts of the spectrum was calculated by "Prism Dispersion Formula".

The experiment results are as follows:

1) The emission from a Black body at any temperature is composed of Radiation from all wavelengths.

2) At a given temperature, the energy is not uniformly distributed. As the temperature of the black body increases, the intensity of radiation for each wavelength increases. This shows that the total amount of energy is radiated per unit area per unit time increases with rise of temperature.

i.e., T 𝛼 Eƛ

3) The total energy of radiation at any temperature is given by the area between the curve corresponding to that temperature and horizontal axis. The increase in area found in accordance with Stefans law.

4) The amount of radiant energy emitted is small at very short and very long wavelengths. At a particular temperature, the spectral radiance Eƛ is maximum at particular wavelength ƛm. Most of the energy is emitted at wavelengths not very  different from ƛm.

5) The wavelength corresponding to the maximum energy represented by the peak of the curve shifts towards shorter wavelengths as the temperature increases. This is called Wiens Displacement. According to this law ƛm x T = constant.

This shows that as the temperature is increased, the black body emits the radiation of shorter wavelengths such that the product of temperature 'T' and maximum wavelength ƛm is a constant. 

The constant is called Wiens Displacement constant and has value 0.2896 x 10⁻² mK. 

There is change in wavelength due to Doppler effect.

Laws Related to Black Body:

a) Kirchoffs Law
b) Stefan-Boltzmann law
c) Wiens Law
d) Rayleigh-Jeans Law
e) Plancks Law

Important points to be noted:

i)  Wiens formula agrees in short wavelength region.
ii)  Rayleigh-Jeans formula agrees for long wavelength region.
iii) Plancks formula covers the entire region.
iv) When radiation is passed through a black body is passed through a prism, acontinuous spectrum is obtained. The energy is distributed in various wavelengths varying from 0 to infinity.
v) The law that connects the intensity with the wavelength is known as law of distribution of intensity of black body radiation.
vi) According to Stefans law, u=𝝈T⁴ where 𝝈 is Stefans constant and 'u' is energy density.

Spectral Energy Density, Total Energy Density, Emmisive Power & Absorptive Power

Spectral Energy Density: 

Spectral Energy Density for a particular wave length is the energy per unit volume per unit range of wavelength.

Total Energy Density:

Total Energy Density of Thermal Radiation at any point is the total radiant energy per unit volume around that point due to all wavelengths.

Emmisive Power:

The emmisive power of a body at a given temperature and for a given wavelength, is defined as the ratio of the radiant energy absorbed for second by unit surface area of the body per unit wavelength range.

Absorptive Power

The absorptive power of a body at a given temperature and wavelength is defined as the ratio of radiant energy absorbed per second by unit surface area of the body to the total energy falling per second on the same area.   

Concept of Thermodynamics - Zeroeth Law of Thermodynamics

For a system to be in thermodynamic equilibrium the following conditions must be full filled:-

i) Mechanical equilibrium

ii) Thermal equilibrium

iii) Chemical equilibrium

Mechanical equilibrium:

When there is no unbalanced force between system and its surroundings, the system is said to be in mechanical equilibrium.

Thermal equilibrium:

When the temperature in all parts of system is same as that of surroundings, the system is said to be in thermal equilibrium.

Chemical equilibrium:

If the chemical composition is same throughout the system and surroundings it is said to be in chemical equilibrium.

Zeroeth Law of Thermodynamics:

This law was first enunciated by RH Flower in 1831. According to this law when two systems ‘A’ and ‘B’ are in thermal equilibrium with another system ‘C’ then ‘A’ and ‘B’ will also be in thermal equilibrium.

What does First Law of Thermodynamics infer us?

• It is impossible to derive any work without expenditure of an equivalent amount of energy in some other forms. 

• Heat absorbed by the system should be taken positive. Heat rejected by the system should be taken negative. 

• For an ideal gas the total kinetic energy (KE) of all its molecules is called internal energy(U). For such a gas the internal energy depends only on Temperature.

What is ENTROPY - Very important Points to be noted

1) The thermal property which remains constant during an adiabatic process is called as entropy.
     i.e. dQ/T= constant

2) It is a measure of randomness or disorderliness of molecules.

3) It is independent of the path of thermal cycle.

4) The increase in entropy implies transition from ordered state to disorder state.

5) It is an index of unavailable energy of a system.

6) Entropy could also be termed as thermal inertia since more entropy results in less amount of heat energy being converted into work.

7) The increase in Entropy of a system implies transition of thermal energy from more available energy to less available form for conversion into work.

8) The net change in entropy is zero for any reversible cycle. This statement is called as clausius theorem.

9) Clausius Theorem: - The sum of quantities of heat transfer during the isothermal change divided     by absolute temperature of the isothermal in a reversible cycle is zero. Entropy changes linearly in isothermal expansion and remains constant in adiabatic expansion or compression but decreases in isothermal compression.

The shape of Temperature (T) - Entropy (S) diagram (Tephigram) is rectangle.

10) Entropy increases in irreversible process.

11) Definition of second law of thermodynamics in terms of entropy

”Every chemical or physical or natural process in nature takes place in such a manner that total entropy increases or remains constant".

12) The principle of "degradation of energy" states that the available energy tending towards zero.