There are three laws of thermodynamics, which are given below

1. Zeroth Law of Thermodynamics

2. First law of Thermodynamics

3. Second Law of Thermodynamics

• This law was formulated by RH Fowler in 1931.

• The Zeroth law of thermodynamics states that if two system A and B are separately in thermal equilibrium with a third system C, then A and B are in thermal equilibrium with each other.

• This law is based on law of conservation of energy. If `deltaQ` is heat supplied to a thermodynamical system and `deltaW` is work done by the thermodynamical system and resulting `deltaU` is the change in internal energy, then

`delta Q = delta W + delta U`

• This equation is the first law of thermodynamics. It is the mathematical statement of 1st law of thermodynamics.

• First law of thermodynamics is one form of law of conservation of energy because the heat supplied is converted into internal energy and work.

`text(Sign Conventions for First Law of Thermodynamics)`
`deltaQ,deltaW` and `deltaU` must be in the same units.
* Heat supplied to the system = Positive
* Heat rejected by the system = Negative
* Work done by the system = Positive
* Work done on the system = Negative
* If temperature increases, `deltaU` = Positive
* If temperature decreases, `deltaU` = Negative

We are going to discuss different types of thermodynamics processes.

1. Reversible and Irreversible Processes
2. Isothermal Process
3. Adiabatic Process
4. Isobaric Process
5. lsochoric Process
6. Cyclic Process

• A reversible process means, if a process takes up the path AB (as shown in figure), then on reversing the conditions it comes back by BA.

• A thermal process could be reversible, if the change is extremely small (infinitesimally small).

• In irreversible process, one will not reach back to A, if the process AB has occurred.

• In this process, temperature of the system is kept constant during the change of state.

• As `Q = n C_(iso) dT => C_(iso) = Q/(ndT) = oo` , i.e. molar heat capacity for an isothermal process is infinity.

• From `dU = nC_v dT` as `dT = 0`, so `dU = 0` , i.e internal energy is constant.

• Gas equation is pV = constant.

• From first law of thermodynamics, dQ = dW i.e. heat given to the system is equal to the work done by system on the surroundings.
`W = nRT ln (V_f/V_i ) = nRT ln (p_i/p_f)`

• After differentiating pV = constant:, we have `(dp)/(dV) = - p/V` ( slope of p-V curve ) and `(-dp)/(dV//V) = p`, (fig.)
i.e bulk modulus of a gas in isothermal process, B = p

• p-V curve is a rectangular hyperbola.

• In this process, no heat exchange takes place between the system and the surroundings, i.e. dQ = 0 or Q = constant

• From dQ = nCdT, `C_(ad) = 0 ` as `dQ = 0`, i.e. molar heat capacity for an adiabatic process is zero.

• From first law, dU = -dW i.e. work done by the system is equal to decrease in internal energy. When a system expands adiabatically, work done is positive and hence internal energy decreases i.e. the system cools down and vice-versa.

• Gas equation is `pV^(gamma) = ` constant. Gas equation can be written in many other ways as `TV^(gamma -1) = ` constant or `p^(1 -gamma) T^(gamma) = ` constant , where `gamma = (C_p)/(C_V)`.

• Work done in an adiabatic process is `W = (nR(T_1 - T_2))/(gamma -1) = (p_1V_1 - p_2V_2)/(gamma -1)`

• Using `pV = nRT` and `pV^(gamma) = ` constant , we can have `(dp)/(dV) = -(gammap)/V`i.e slope of `p -V` curve in an adiabatic process is `gamma` times the slope of `p-V` curve in isothermal process.

• This is the process in which pressure is kept constant.

• Molar heat capacity of the process is `C_P` and `dQ = nC_PdT`

• `dU = nC_VdT`

• From the first law thermodynamics, `dQ = dU + dW ; dW = pDV = n RdT`

`=> W = p (V_f - V_i ) = n R ( T_f - T_i)`

• Gas equation is `V/T = ` constant

• p-V curve is a straight line parallel to the volume axis.

• This is the process in which volume is kept constant.

• `dQ = nC_V dT`, molar heat capacity for isochoric process is `C_V`.

• Volume is constant, so dW = 0

• From the first law of thermodynamics, dQ = dU. As heat is supplied to the system, internal energy increases and hence the temperature increases.

• Gas equation is `p/T =` constant.

• p-V curve is a straight line parallel to the pressure axis.

In cyclic process, final state of gas is same as the initial state of gas. For one complete cycle process, `dU =0 `

Work done by the gas is equal to the area enclosed by the p-V curve.

Here, net heat in the process is given by

Net heat = Total heat supplied + Total heat rejected

Efficiency of cyclic process `eta = text(total work done in cycle)/text( Total heat supplied) xx 100 %`

• It is molecular disorder of system and it is thermodynamic function depending only on temperature of system.

• `Delta S = text( heat absorbed)/text( absolute temperature ) => Delta S = (Delta Q)/T`

• Entropy is the thermodynamical function which remains unchanged in an adiabatic process.

Second law of thermodynamics tells us whether in a given process conservation of energy will actually take place or not. This law gives the direction of heat flow. It can be stated as follows

(i) `text(Clausius statement)`
It is impossible to make any such machine that can transfer heat from an object with low temperature to an object with high temperature without any external source.

(ii) `text(Kelvin statement)`
It is impossible to obtain work continuously by cooling an object below the temperature of its surroundings.

(iii) `text(Kelvin-Planck statement)`
It is impossible to construct any such machine that works on a cyclic process and absorbs heat from a source, converts all that heat into work and rejects no heat to sink.

• It is a device which is used to convert heat energy into mechanical energy, in a cyclic process.

• Components of a heat engine are
(i) A body at higher temperature `T_1` from which heat is extracted is called the source.
(ii) Body of the engine contains a working substance which performs mechanical work, when heat is supplied to it.
(iii) A body at lower temperature `T_2` to which heat can be rejected is called the sink.

• Efficiency of heat engine (`eta`) is defined as the fraction of total heat supplied (`Q_1`) to the engine which is converted into work (W).

• Mathematically, `eta=W/Q`
or `eta=(Q_1 - Q_2)/Q_1 = 1- (Q_2)/(Q_1) = 1- (T_2)/T_1` `[because (Q-2)/(Q_1) = (T_2) / (T_1)]`

• Carnot cycle is the ideal cycle of operation of a heat engine, devised by Nicholas Leonard Sadi Carnot. This consists of the following four stages.

(i) Isothermal expansion (heat absorbed)
(ii) Adiabatic expansion (work done is positive, `W_text(expansion)` )
(iii) Isothermal compression (heat released)
(iv) Adiabatic compression ( work done is negative, `W_text(compression)`)

• Efficiency of Carnot engine is given by

`eta = (1 - T_2/T_1) xx 100 %`

where , `T_2 = ` temperature of cold body or sink
and `T_1 =` temperature of hot body or source

• Also , `eta = W/Q_1 xx 100 %` `= (Q_1 - Q_2)/Q_1 xx 100 %`

• For Carnot cycle , `Q_1/Q_2 = T_1/T_2`
where `Q_1 = ` heat absorbed and `Q_2 =` heat given

No heat engine operating between two given temperatures can be more efficient than a Carnot engine.

• Refrigerator is a device which takes heat from a cold body, work is done on it and the work done together with the heat absorbed is rejected to the source.

• An ideal refrigerator can be regarded as an ideal heat engine working in the reverse direction.

`text(Coefficient of Performance of a Refrigerator)(beta)`
It is defined as the ratio of quantity of heat removed per cycle (`Q_2`) to the work done on the working substance per cycle to remove this heat.
`beta=(Q_2)/W =(Q_2)/(Q_1 - Q_2)` or `beta=(T_2)/(T_1 -T_2) = (1-eta)/eta`

As we know that heat flows from the body at higher temperature to the body at lower temperature, this flow of heat is known as transfer of heat from one place to another. There are three process by which transmission of heat takes place.

(i) `text(Conduction)`
• Conduction is that process of transmission of heat in which heat goes from one particle to another particle of substance, but no particle leaves its position.

• In solids, transmission of heat takes place by conduction process.

• All metals are good conductor of heat.

• Good absorbers are always also good radiators.

• Cooking utensils are provided with wooden or ebonite handles, since wood or ebonite is a bad conductor of heat.

• Silver is the best conductor of heat.

(ii) `text(Convection)`
• Convection is that process of transmission of heat in which particles of substance goes to another place after taking heat from the source and other particles come to their place.

• In liquids and gases, transmission of heat takes place by convection process.

• Land and see breezes are due to convection.

• The chimney used in a kitchen or in a factory is based on the convection.

• In rooms ventilators are provided to escape the hot air by convection.

(iii) `text(Radiation)`
• Radiation is that process of transmission of heat in which there is no need of medium for transfer of heat.

• It is the quickest way of transmission of heat.

• Heat from the sun comes to the earth by radiation.

`text(Stable State)`
The state of material in which material cannot absorb or emit the heat, known as stable state of material.

`text(Isothermal Surface)`
The conductor which have some temperature at all the points, known as isothermal surface.

`text(Temperature Gradient)`
The rate of change in temperature with the distance known as temperature gradient. Its unit is °C /meter.
Temperature gradient `= (Q_1 - Q_2)/r` where `Q_2 > Q_1`

• The ability of material to conduct the heat through it, is known as thermal conductivity. Thus, heat conduction is defined as the time rate of heat flow in a material for a given temperature difference.

Consider a metal rod of length `l` and area of cross-section A. Let the ends of the rod arc at the temperatures `T_1` and `T_2`

Then, Rate of flow of heat (H) `prop` Temperature difference `Delta T`
`Hprop=` Time for which the heat flows (t)
`Hprop=` Area of cross section (A)
`Hprop=` `1/text(length of the rod)=1/L`.

Thus, the rate of heat transfer is given by
Rate of heat transfer `= (Delta Q)/(Delta t) = (KA (T_1 - T_2))/L => H = KA (Delta T)/L`

Also , `H = Q/t`

`because ` Heat transfer , `Q = K A (DeltaT)/A * t`

Here, K = coefficient of thermal conductivity of material of rod.

• The greater value of K implies that material will conduced the heat more rapidly.

• The SI unit of K is `Js^-1m^-1K^-1` or `Wm^-1K^-1`.

• The value of thermal conductivity vary slightly with temperature, but it can be considered to be constant over normal temperature range.

• If `A = 1, T_1 - T_2 = Delta T = 1, L = 1` and t = 1, then `Q = K`
Hence, the coefficient of thermal conductivity of a material may be defined as the quantity of heat that flows per unit time through a unit cube of the material, when its opposite faces are kept at a temperature difference of one degree.

• The rate of flow of heat is known as heat current. It is denoted by H.

Thus, `H = (Delta Q ) /(Delta t) = KA ((T_1 -T_2))/L = (T_1 -T_2)/((L/(KA)))`

• Thermal resistance, `R = (Delta T)/H = (T_1 - T_2)/H = L/(KA)`

`:.` Thermal resistance , `R = L/(KA)`

• It is just resemble to current, `i = ( V_1 -V_2)/R`

where `V_1 - V_2 =` voltage difference and R = resistance.

So, the terms `(T_1 -T_2)/(L//KA)` and `L/(KA)` can be treated as thermal current (heat flow ) and thermal resistance, respectively.

`text(Emissive Power) (e)`
It is defined as the amount of heat radiated by unit area of the surface in one second at a given temperature and for given wavelengths. Its unit is J/m²s.

`text(Emissivity) (epsi)`
The ratio of total emissive power of the body to the total emissive power of a perfectly black body at that temperature is called emissivity, represented as `epsi = e/E`

`Atext(bsorptive Power) (a)`
It is defined as the ratio of absorbed radiation and total incident radiation. It has no unit.
`a = text(Energy absorbed)/text(Energy incident)`

`text(Spectral Emissive Power)` (`e_lamda)`
Spectral emissive power (`e_lamda`) is the amount of heat radiated by unit area of body in one second in unit spectral region at particular wavelength `lamda`.
Its unit is J/m² second A.

`text(Spectral Absorptive Power)`
It is defined as the ratio of radiations absorbed by the surface in unit spectral region at wavelength `lamda`, to the total amount of radiations incident on it.

A perfectly black body is one which absorbs completely all the radiations of whatever wavelength incident upon it.
Since, it neither reflect nor transmit any radiation, it appears black whatever the colour of the incident radiation may be.

At any temperature and for a particular wavelength, the ratio of emissive power to the absorptive power of all substances is same and it is equal to the emissive power of a perfectly black body.
i.e `e_lamda/a_lamda = E_lamda`

According to this law, the amount of heat radiated by unit area of surface in one second, is directly proportional to the fourth power of absolute temperature of the body.

`E prop T^4` or `E = sigma T^4`

where , `sigma` is stefan's constant. The unit of `sigma` is `Jm^-2s^-1K^-4` or `Wm^-2K^-4`
and its value is ` 5.67 xx 10^-8 Wm^-2K^-4`

According to this law, the rate of cooling of a body is directly proportional to the temperature difference of body and its surroundings.
e.g. Hot water takes much less time in cooling from 100°C to 95°C than from 20°C to 15°C.
If hot water and fresh tap-water are kept in a refrigerator, the rate of cooling of hot water will be faster than the tap-water.

According to this law, at a particular temperature of perfectly black body, the product of maximum wavelength (`lamda_m`) and absolute temperature T is constant.
i.e. `lamda_mT = ` constant or `lamda_m = b`
where, the value of b is `2.9 xx 10^-3 mK`.

This is called Wien's displacement law.
It is used to compute the temperature of the Sun or of the Stars.