Physics Chapter (12) Heat and Thermodynamics

Heat

Heat was considered a fluid named as CALORIC. Hot bodies contain more caloric than cold bodies.

Count rum-ford challenged this theory by producing heat by friction. Joule and other scientists proved that heat is form of energy. The unit of heat is joule. According to Kinetic Molecular Theory “the sum of all microscopic energies of all molecules in a body is called amount of heat”

Temperature

The degree of hotness and coldness in a body is called temperature.

Scales of Temperature

The lower fixed point is 0 ⁰C (zero degree Celsius) and upper fixed point is 100 ⁰C (degree Celsius).

The upper fixed point is the temperature of steam at 100 degree Celsius.

There are three main scales used to measure temperature.

• Celsius scale
• Fahrenheit scale
• Kelvin scale or absolute scale

Celsius scale, the lower fixed point is 0 (zero) degrees and upper fixed point is 100 degree Celsius.

On Fahrenheit scale, the lower fixed point 32 degree Fahrenheit and upper fixed point is point is 212 Fahrenheit.

On Kelvin scale the lowest temperature is -273 ⁰C.

⁰C = 5/9(F-32) the Fahrenheit scale converted in to Centigrade (Celsius) scale.

⁰F = 9/5 C + 32 the centigrade scale is converted to Fahrenheit scale.

 K = ⁰C + 273 the absolute scale of centigrade (Kelvin scale).

 R = ⁰F  + 460 the absolute scale of Fahrenheit (Rankin scale). 

Both Fahrenheit and Centigrade scale coincide at  40^{0 .}

Thermal Expansion

Expansion of length of solids on heating is called linear expansion.

Change in lengths ∆L = αL₀∆T

Where α = Coefficient of change in length

Lo = Initial co-efficient.

Co-efficient of linear expansion

The change in length per unit length per degree rise in temperature.

 α   = ∆L / L₀∆T

Its value depends only upon nature of materials.

 α = L₂ – L₁/ L₀∆T                       α L₀∆T = L – L₀

L = L₀ + α L₀∆T

L = L₀ (1+ α ∆T)

L = Final length

Volumetric Expansion

The three dimensional expansion in solids, liquids and gases is cubical expansion.

Change in volume ∆V = βV₀∆T

Final Volume V =   V₀ (1 + β∆T)

Co-efficient of Volumetric Expansion

The change in volume per unit volume rise in temperature per degree rise in temperature is called co-efficient of volumetric expansion.

i.e.

 β = ∆V/ V₀ ∆T

Its value depends only upon nature of material.

Relation between α and β

Co-efficient of volumetric expansion is three times that of co-efficient of linear expansion. 

  α = 3 β

Bimetallic Strip

When two strips of different metals (iron & brass) are attached rigidly side of side then such type of device is called bimetallic strip.

Examples of Bimetallic strips are

1-   The gas oven thermostat

2-   The electric thermostat

3-   Electric fire alarm

Anomalous Expansion of Water

When water is heated from 0⁰C to 4⁰C, it contracts. When water is cooled from 4⁰C to 0⁰C, it expands.

Transfer of Heat

Conduction

It is the process, in which heat is transferred from atom to atom without the substance.

It takes place in solids. Conduction occurs at different rates in different materials.

Convection

It is the process, in which heat is transferred by the actual movement of molecules. It is peculiar to fluids i.e. liquids and gases.

Radiation

It is process, which does not require any material medium to transfer heat.

In this process, heat energy is carried by infra-red electromagnetic waves.

The heat energy from the sun reaches us by radiation.

Gas Laws

Boyle’s Law

Boyle’s law states that “for given mass of gas, at constant temperature”, the volume is inversely proportional is pressure applied i.e. PV= constant.

Charles’s Law

Charles’s states that, “for given mass of a gas, at constant pressure, the volume is directly proportional to temperature i.e. V/T= Constant.

General Gas Law

General gas law is combination of Boyle’s law and Avogadro’s law i.e. the two equations are used as, General gas equations which are:

P₁V₂/T₁   =   P₂V₂/T₂

PV =   nRT

Kinetic Theory of Gases

On the basis of Kinetic theory of matter, the gases have following properties.

·       A gas consists of identical molecules composed of an atom or group of atoms.

·       At S.T.P, 3×10²⁵ molecules are in a cubic meter.

·       Molecules are separated at large distance.

·       Molecules move randomly in straight line, and made elastic collision with walls and without another.

·       Molecules exert no force on one another except during collisions.

Pressure of a Gas

The pressure exerted by the molecules moving with average velocity v is P = 1/3 ρ v² where ρ = density of gas.

Root mean square Velocity

Root mean square velocity (V_rms) of a gas can be calculated as

V_rms =  (3P/ρ)^1/2               OR              (3KT/m)^1/2

Relation between the average Translational K.E and Absolute Temperature

The average translational kinetic energy of molecule is directly proportional to the absolute temperature.

1/2mv² = 3/2 KT      for per mole = 3/2 RT

Specific Heat

Heat Capacity

The amount of heat required to raised the temperature of a substance through 1 K i.e. C = ∆Q/ ∆t

 It is measured in J/Kg

Specific Heat Capacity

The amount of heat required to raise the temperature to raise the temperature of unit mass of a substance to unit degree rise in temperature, i.e.  C =∆Q/m∆T

It is measured in J/Kg.K e.g. the specific heat of water is 4200 J/Kg.K

Molar Specific Heat

It is the quantity of heat required to raise the temperature of one mole of a substance through 1K.

C_mol = ∆Q/n∆T.    Its unit is J/mole K

There are two kinds of molar specific heats of a gas

·       Molar specific heat at constant volume.

·       Molar specific at constant pressure.

The heat capacity of an ideal gas at constant pressure is greater than the capacity constant volume.

i.e. C_P – C_V = R  R= universal gas constant = 8.313 J /mol K.

Where C_P is the specific heat of material at constant pressure and C_V is the specific heat of the material at constant volume.

For mono atomic gases, C_P = 5/2R   and C_V = 3/2R and γ =1.66

Melting Point

The temperature at which a solid changes into liquid is called melting point.

Freezing Point

The temperature at which the liquid changes into solids is called freezing point.

Latent Heat of Fusion

It is the quantity of heat required to transform one Kg of ice completely into water at 0⁰C. The latent heat of fusion is 3.36 × 10⁵J/kg.

Latent Heat of Vaporization

It is the quantity of heat required to transform 1 kg water into vapours at its boiling point 100⁰C.

The latent heat steam is 2.26 ×10⁶ J/kg.

Calorie

It is the unit of heat, 1 calorie = 4.2 Joules

Effect of Pressure on Melting Point

Increase of pressure lowers the freezing point of water.

Regelation

The process in which ice or snow melts under pressure and refreezes again when pressure is removed is known regelation.

Effect of Pressure on Boiling Point

Decrease in pressure lowers the boiling point of liquids.

Evaporation

The changing of liquids into vapours without boiling is called evaporation. It depends on the following factors.

·       Nature of liquids

·       Temperature of liquid

·       Surface area of liquid

·       Dryness of air

·       Wind speed

·       Air pressure on the surface of liquids

Thermodynamics

Thermodynamics is the field related to the transformation of heat energy into other types of energies and vice versa.

First law of the Thermodynamics

First law of thermodynamics states that the amount of heat ∆Q supplied to a system is conserved in doing some external work ∆W as well as to increase the internal energy ∆U.

i.e. ∆Q = ∆U + ∆W

Ø Application of First law of thermodynamics

Isobaric Process

This is process which takes place at constant pressure.

ü In an isobaric process a gas in a cylindrical vessel with frictionless air tight piston expands on heating and the piston moves to keep the pressure unchanged.

ü The work done by the gas is W = P∆V. Where ∆V is the increase in volume.

ü The first law of thermodynamics in isobaric process becomes

                ∆Q = ∆U + P∆V

         

Isochoric Process

Isochoric process is the process in which the volume of a system remains constant.

Since the volume is constant, therefore the change in volume is zero and so that the work done W.

.^.. W = P∆V=0

·       The first law of thermodynamics in isochoric process becomes

       ∆Q = ∆U

·       For isochoric process, first law thermodynamics can be state as ‘the energy provide to a system is entirely utilized in changing its internal energy.

Isothermal Process

If the temperature of the system remains constant throughout the process, it is called an isothermal process.

·       The internal energy of the gas does not change during isothermal process i.e. ∆U = 0

·       The first law of thermodynamics for an isothermal process                 ∆Q = W

·       For isothermal process, the first law of thermodynamics can be stated ‘the energy transferred to the system is entirely utilized in work done. Boyle’s law is PV = constant.

            

     

Adiabatic Process

The process which no heat into or out of the system is called an adiabatic process. During an adiabatic process, the substance is perfectly insulated from the surrounding such that it does not exchange heat energy from the surroundings i.e. ∆Q = 0

·       The first law of thermodynamics from an adiabatic process becomes  ∆U + ∆W = 0

                      OR

                           -∆U = ∆W

For adiabatic process, the first law of thermodynamics can be stated as ‘the work done on the system in an adiabatic process causes the change in internal energy of the system.

·       Boyle’s law is PV^γ = constant

Second law of thermodynamics

This law consists of two statements.

Kelvin Statement:

It is impossible to design a heat engine which can supply a continuous work by taking heat from a source without losing into the sink.

Clausius statement:

It is impossible to design a cold engine which can transfer heat low temperature without using external energy.

Carnot Heat Engine

It is an ideal heat engine, which has the maximum possible efficiency that can be obtained by any heat engine operating in a cycle between the two given reservoirs of heat at different temperatures.

Carnot heat engine is an ideal engine, consists of infinite thermal capacity, a similar cold body, a perfect heat insulator and a cylinder with a working substance. Carnot engine is a reversible engine.

Carnot cycle consist of two isothermal and adiabatic compressions and two expansions.

  η = Output/Input = W/Q₁

 W/Q₁ = Q₁-Q₂/ Q₁ = 1- W/Q₁

Where Q₂ = Heat rejected to sink.

 Q₁ = Heat supplied by source

Efficiency also expressed in terms of temperature η = 1-T2 /T1

Entropy

Entropy is the measure of disorder of a system.

                                 Or

The unavailability of energy from a system is called entropy.

Entropy or disorder always increase or remains constant.

Second law of thermodynamics also state as “when an isolated system under goes a change, the disorder in the system increases.

Change in entropy is ∆S =  ∆Q/T1

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