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### Thermodynamics

Zeroth law of thermodynamics : The Zeroth Law of Thermodynamics states that if two bodies are each in thermal equilibrium with some third body, then they are also in equilibrium with each other.

First Law of Thermodynamics : The first law of thermodynamics states that the change in internal energy of a system equals the net heat transfer into the system minus the net work done by the system.

ΔQ = ΔU + ΔW

Application of first law of thermodynamics:-

• Cooling caused in adiabatic process:- dT = PdV/Cv
• Melting:- dU = mLf
• Boiling:- dU = mLv – P(Vf -Vi)
• Mayer’s formula:- Cp - Cv = R

Second law of thermodynamics:-

• Clausius statement:- Heat cannot flow from a cold body to a hot body without the performance of work by some external agency.
• Kelvin’s statement:- It is impossible to obtain a continuous supply of energy by cooling a body below the coldest of its surroundings.
• Planck’s statement:- It is impossible to extract heat from a single body and convert the whole of it into work.

Carnot engine – Carnot’s reverse cycle:-

Carnot devised an ideal engine which is based on a reversible cycle of four operations in succession : isothermal expansion, adiabatic expansion, isothermal compression and adiabatic compression.

• First stroke (isothermal expansion)
• Third stroke (isothermal compression)
• Total work done in one cycle : W = W1+ W2+ W3+ W4 = R (T1-T2) loge (V2/V1)

Heat Engine

Heat engine is a device to convert heat into work.

It have three parts

• A high temperature reservoir ( T1)
• A sink or low temperature reservoir ( T2)
• A working substance

Efficiency of Heat Engine

Efficiency = $Work Done \over Heat taken from substance$ = ${Q_1 - Q_2} \over Q_1$ = $1 - {Q_2 \over Q_1}$

Efficiency of Carnot engine,

$η = 1 - {Q_2 \over Q_1}$

$η = 1 - {T_2 \over T_1}$

Thermodynamic Process:- A process by which one or more parameters of thermodynamic system undergo a change is called a thermodynamic process or a thermodynamic change. P-V diagram of isothermal, isobaric, isochoric and adiabatic process in a single figure.

Isothermal process:- The process in which change in pressure and volume takes place at a constant temperature, is called a isothermal change. It may be noted that in such a change total amount of heat of the system does not remain constant. It follow Boyle's Law

Isobaric process:- The process in which change in volume and temperature of a gas take place at a constant pressure is called an isobaric process.

Isochoric process:- The process in which changes in pressure and temperature take place in such a way that the volume of the system remains constant

Adiabatic process:- The process in which change in pressure and volume and temperature takes place without any heat entering or leaving the system

Quasi-static process:- The process in which change in any of the parameters take place at such a slow speed that the values of P,V, and T can be taken to be, practically, constant, is called a quasi-static process.

Cyclic process:- In a system in which the parameters acquire the original values

Free expansion:- Such an expansion in which no external work is done and the total internal energy of the system remains constant

Process Constant Parameter Equation First Law of Thermodynamic
Isothermal Temperature PV = constant ΔU = 0
ΔQ = ΔW
Adiabatic Total Heat or Entropy PVγ = constant
TVγ-1 = constant
P1-γTγ
ΔQ = 0
ΔU = -ΔW
Isobaric Pressure P = constant
${V \over T}$ = constant
ΔW = PΔV
ΔQ = ΔU + PΔV
Isochoric Volume V = constant
${P \over T}$ = constant
ΔW = 0
ΔQ = ΔU

### Kinetic Therory of Gas

IDEAL GASIn an ideal gas, we assume that molecules are point masses and there is no mutual attraction between them.

BOYLE’S LAW

According to Boyle’s law for a given mass of ideal gas, the pressure of a ideal gas is inversely proportional to the volume at constant temperature

$PV = constant$

CHARLE’S LAW

For a given mass, the volume of a ideal gas is proportional to temperature at a constant pressure

${V \over T }= constant$

GAY-LUSSAC’S LAW

For a given mass of ideal gas, the pressure is proportional to temperature at constant volume

${P \over T} = constant$

According to Avogadro’s law, the number of molecules of all gases are same at same temperature, pressure and volume

The value of Avogadro number is 6.02 × 1023 molecules.

GRAHAM’S LAW

• At constant temperature and pressure, the rms speed of diffusion of two gases is inversely proportional to the square root of the relative density

$r ∝ {1\over \sqrt{d}}$

• According to Graham’s law, the rate of diffusion of a gas is inversely proportional to the square root of its density, provided pressure and temperature are constant

DALTON’S LAW The pressure exerted by a gaseous mixture is equal to sum of partial pressure of each component gases present in the mixture,

i.e., P = P1 + P2 + P3+.................. Pn

Postulates of Kinetic theory of gases (1) A gas consists of a very large number of molecules. Each one is a perfectly identical elastic sphere. (2) The molecules of a gas are in a state of continuous and random motion. They move in all directions with all possible velocities. (3) The size of each molecule is very small as compared to the distance between them. Hence, the volume occupied by the molecule is negligible in comparison to the volume of the gas. (4) There is no force of attraction or repulsion between the molecules and the walls of the container. (5) The collisions of the molecules among themselves and with the walls of the container are perfectly elastic. Therefore, momentum and kinetic energy of the molecules are conserved during collisions. (6) A molecule moves along a straight line between two successive collisions and the average distance travelled between two successive collisions is called the mean free path of the molecules. (7) The collisions are almost instantaneous (i.e) the time of collision of two molecules is negligible as compared to the time interval between two successive collisions.

### Transfer of Heat

Conduction Conduction is that mode of transmission of heat by which heat travels, through an unequally heated body, from the hot end to the cold end, from particle to particle, the particles themselves remaining at their mean positions.

Convection:- It is defined as that mode of transmission of heat by which heat travels from one part of a body to another by the actual motion of the heated particles of the body.

Radiation:- It is defined as that mode of transmission of heat in which heat travels from hot body to cold body in straight lines without heating the intervening medium.

Stegan-BoltzMann's Law: According to this law, the amount of radiation emiited per unit time from an area A of a black body at absolute temperature T is directly proportional to the Fourth power of temperature

u = AT4

Black Body: A perfectly black body is that which absorbs completely the radiations of all wavelengths incident on it.

### Hygrometry

The branch of physics which deals with the study and measurement of water vapour present in the atmosphere is called hygrometry.

Boiling Point : The boiling point of a substance is the temperature at which the vapor pressure of a liquid equals the pressure surrounding the liquid and the liquid changes into a vapor.

Triple Point : triple point of a substance is the temperature and pressure at which the three phases (gas, liquid, and solid) of that substance coexist in thermodynamic equilibrium.

Dew PointThe dew point is the temperature at which air is saturated with water vapor

Absolute humidity : Absolute humidity is the quality of water vapor in the wet air of unit volume (1 m3)

Relative humidity Relative Humidity tells us how much water vapor is in the air, compared to how much it could hold at that temperature. It is shown as a percent. For example, a relative humidity of 50 percent means the air is holding one half of the water vapor it can hold.

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