HEAT

CHAPTER – 11

HEAT

DEFINITION

Total Kinetic energy of a body is known as HEAT.

OR

Transfer of energy from a hot body to a cold one is termed as Heat.

Heat is measured by using an measurement centimeter.

UNITSSince heat is a force of energy therefore its unit is Joule (J).

TEMPERATURE

DEFINITION

The average kinetic energy of a body is known as Temperature.

OR

The quantitative determination of degree of hotness may be termed as Temperature.

SCALES OF TEMPERATUREThere are three main scales of temperature.1. Celsius Scale2. Fahrenheit Scale3. Kelvin ScaleCelsius and Fahrenheit scales are also known as Scales of Graduation.

1. Celsius ScaleThe melting point of ice and boiling point of water at standard pressure (76cm of Hg) taken to be two fixed points. On the Celsius (centigrade) scale the interval between these two fixed points is divided into hundred equal parts. Each part thus represents one degree Celsius (1°C). This scale was suggested by Celsius in 1742.Mathematically,

°C = K – 273OR°C = 5/9 (°F – 32)

2. Fahrenheit ScaleThe melting point of ice and boiling of water at standard pressure (76cm of Hg) are taken to be two fixed points. On Fahrenheit scale the lower fixed point is marked 32 and upper fixed point 212. The interval between them is equally divided into 180 parts. Each part represents one degree Fahrenheit (1°F).Mathematically,°F = 9/5 (°C + 32)

3. Kelvin ScaleThe lowest temperature on Kelvin Scale is -273°C. Thus 0° on Celsius scale will be 273 on Kelvin scale written as 273K and 100 on Celsius scale will be 373K. The size of Celsius and Kelvin scales are same.Mathematically,K = °C + 273

THERMAL EQUILIBRIUM

Heat flows from hot body to cold body till the temperature of the bodies becomes same, then they are said to be in Thermal Equilibrium.

THERMAL EXPANSION

DEFINITION

The phenomenon due to which solid experience a change in its length, volume or area on heating is known as Thermal Expansion.

ExplanationIf we supply some amount of heat to any substance then size or shape of the substance will increase. This increment is known as Thermal Expansion. Thermal expansion is due to the increment of the amplitudes of the molecules.

Types of Thermal ExpansionThere are three types of Thermal Expansion.1. Linear Expansion2. Superficial Expansion3. Volumetric Expansion.

1. Linear Expansion.If we supply some amount of heat to any rod, then the length of the rod, then the length of the rod will increase. Such increment is known as Linear Expansion.

2. Superficial Expansion.If we apply some amount of heat to any square or rectangle then area of the square or rectangle will increase. Such increment is known as Superficial Expansion.

3. Volumetric Expansion.If we apply some amount of heat to any cube, then the volume of the cube will increase. Such increment is known as Volumetric Expansion.

COEFFICIENT OF LINEAR EXPANSION

CONSIDERATIONLet Lo be the initial length of rod at t1 °C. If we increase the temperature from t1 °C to t2 °C, then length of the rod will increase. This increment in length is denoted by ΔL. The increment in length depends upon the following two factors.1. Original Length (Lo)2. Difference in temperature Δt

DerivationThe increment in length is directly proportional to the original length and temperature difference.Mathematically,ΔL ∞ Lo —– (I)ΔL ∞ Δt —– (II)Combining eq (I) and (II), we getΔL ∞ LoΔt=> ΔL = ∞LoΔtWhere α is the constant of proportionality and it is known as coefficient of Linear Expansion. It is defined as,It is the increment in length per unit length per degree rise in temperature.Its unit is 1/°C or °C. If Lt is the total length, thenLt = Lo + ΔL=> Lt = Lo + αLoΔt=> Lt = Lo (1 + αΔt)

COEFFICIENT OF VOLUMETRIC EXPANSION

ConsiderationLet Vo be the initial length of rod at t1 °C. If we increase the temperature from t1°C to t2°C then length of the rod will increase. This increment in length is denoted by ΔV. The increment in length depends upon the following two factors.3. Original Volume (Lo)4. Difference in temperature Δt

DerivationThe increment in volume is directly proportional to the original volume of temperature difference.Mathematically,

ΔV ∞ Vo —- (I)ΔV ∞ Δt —- (II)Combining eq (I) and (II), we get,ΔV ∞ Vo Δt=> ΔV = βVoΔtWhere β is the constant of proportionality and it is known as coefficient of Volumetric Expansion. It is defined asIt is the increment in volume per unit volume per degree rise in temperature.Its unit is 1/°C or °C-1. If Vt is the total volume thenVt = Vo + ΔV=> Vt = Vo + αβVo Δt=> Vt = Vo (1 + βΔt)

State and Explain Boyle’s Law and Charle’s Law.

INTRODUCTIONGas Laws are the laws, which give relationship between Pressure, Volume, temperature and mass of the gas. There are two gas laws.1. Boyle’s Law2. Charle’s Law

BOYLE’S LAW

Statement 1According to first statement of Boyle’s Law:Volume of the known mass of gas is inversely proportional to the pressure, if temperature is kept constant.Mathematical FormMathematically,V ∞ 1/P=> V = K 1/P=> PV = K (Constant)P1V1 = P2V2 = … = K=> P1V1 = P2V2The above equation is mathematical form of Boyle’s Law.

Statement IIAccording to second statement of Boyle’s Law.The product of the pressure and volume of the known mass of the gas remain constant if the temperature is kept constant.

Statement IIIAccording to third statement of Boyle’s Law.The product of pressure and volume of a gas is directly proportional to the mass of a gas, provided that temperature is kept constant.

Mathematical FormMathematically,PV ∞ m=> PV = Km=> PV/m = K=> P1V1/m1 = P2V2/m2

Limitations of Boyle’s LawBoyle’s Law does not hold good at high pressure, because at high pressure gases convert into liquid or solid.

Graphical RepresentationThe graph between pressure and volume is a curved line, which shows that volume and pressure are inversely proportional to each other.

CHARLE’S LAW

Statement IAccording to first statement of Charle’s Law.Volume of known mass of gas is directly proportional to the absolute temperature, if then pressure is kept constant.Mathematical FormMathematically,V ∞ T=> V = KT=> V/T = KOR=> V1/T1 = V2/T2The above equation is mathematical form of Charles Law.

Statement IIAccording to second statement of Charles Law.The ratio between volume and temperature of the known mass of a gas is always constant, if pressure is kept constant.

Limitations of the LawThis law does not hold good at low temperature because at low temperature gases convert into liquid or solid.

GENERAL GAS EQUATION

It is the combination of Boyle’s law, Charle’s Law and Avogadro’s Law. According to Boyle’s Law.V ∞ 1/P —- (I)According to Charle’s LawV ∞ T —- (II)

According to Avogadro’s LawV ∞ n —- (III)Combining eq (I), eq (II) and eq (III)V α nT/P=> V = RnT/P=> PV = RnT —- (A)Where R is the universal gas constant, We Know thatR = R/NA=> R = KNAWhere K is the Boltzman constant, Its value isK = 1.38 x 10(-23) J/KSubstituting the value of R in eq (A)=> PV = nKNAT=> PV = nNAKTBut nNA = N1 (Total number of molecules), therefore,PV = NtKT=> P = Nt/V KTSince Nt/V = N (Total Number of molecules in a given volume), therefore,P = NKTThe above equation is other form of General Gas Equation.

Qs. What are the basic postulates of Kinetic Molecular Theory pf Gases?

INTRODUCTIONThe properties of matter in bulk can however be predicted on molecular basis by a theory known as Kinetic Molecular theory of gases. The characteristic of this theory are described by some fundamental assumptions, which explained below:

BASIC POSTULATES OF KINETIC MOLECULAR THEORY OF GASES

1. CompositionAll gases are composed of small, spherical solid particle called molecules.

2. Dimension of MoleculesThe dimensions of the molecules is compared to the separation between the molecule is very small.

3. Number of MoleculesAt standard condition, there are 3 x 10(23) molecules in a cubic meter.

4. Pressure of GasGas molecules collide with each other as well as with the wall of the container and exert force on the walls of the container. This force per unit are is known as Pressure.

5. Collision Between the MoleculesThe collision between the molecules is elastic in which momentum and Kinetic energy remains constant.

7. Kinetic Energy of MoleculesIf we increase the temperature of gas molecules, then K.E will also increase. It means that average kinetic energy of the gas molecules is directly proportional to the absolute temperature.

8. Forces Of InterractionThere is no force of attraction or repulsion between the molecules.

9. Law of MechanicsNewtonian mechanics is applicable to the motion of molecules.

THERMODYNAMICS

DEFINITIONSThe branch of Physics that deals with the conversion of heat energy into mechanical energy or work or transformation of work into heat energy is known as Thermodynamics.

Laws of ThermodynamicsThere are two laws of thermodynamics.1. First Law of Thermodynamics2. Second Law of Thermodynamics

State and explain first law of Thermodynamics. What are the application of first law of Thermodynamics?

FIRST LAW OF THERMODYNAMICS

First StatementWhenever heat energy is converted into work or work is transformed into heat energy, the total amount of heat energy is directly proportional to the total amount of work done.

Mathematical Expression

Mathematically,Q ∞ W=> Q = JWWhere J is the mechanical equivalent of heat or joules constant. Its value is 4.2 joules.

Second StatementIf ΔQ is the amount of heat supplied to any system, then this heat will be utilized to increase the internal energy of the system in the work done in order to move the piston.

Mathematical ExpressionMathematically,ΔQ – Au + ΔwThe above equation is the mathematical form of first law of thermodynamics.WhereΔu = Internal energy of the system.Δw = Amount of work done.ΔQ will be positive when heat is supplied to the system and it is negative when heat is rejected by the system.Δw will be positive when work is done by the system and it will be negative when work is done on the system.

Third StatementFor a cyclic process, the heat energy supplied to a system and work done on the system is equal to the sum of heat energy rejected by the system.

Mathematical ExpressionMathematically,Q(IN) + W(IN) = Q(OUT) + W(OUT)Q(IN) – Q(OUT) = W(OUT) + W(IN)ΔQ = ΔW{dQ = {dW{Shows cyclic process

Fourth StatementFor a system and surrounding the total amount of heat energy remains constant

APPLICATIONS OF THE LAWThere are four applications of first law of Thermodynamics.1. Isometric or Isocohric Process.2. Isobaric Process3. Isothermal Process4. Adiabatic Process

1. Isometric or Isocohric ProcessThe process in which volume of the system remains constant is known as Isometric Process.In this process all supplied amount of heat is utilized to increase the internal energy of the system.

Mathematical FormIn this process first law of thermodynamics take the following form.ΔQ = Δu + ΔWBut,ΔW = 0=> ΔQ = Δu = 0=> ΔQ = Δu

2. Isobaric ProcessThe process in which pressure is kept constant is known as isobaric process.In this process, all supplied amount of heat is utilized for the following two functions.i. To increase the internal energy of the system.ii. In work done in order to move the piston upward.

3. Isothermal ProcessA process in which temperature is kept constant is known as Isothermal Process.There are two parts of isothermal process.i. Isothermal Expansionii. Isothermal Compression

i. Isothermal ExpansionIn this process cyclinder is placed on a source and piston is allowed to move upward. When we do so temperature and pressure of the working substance will decrease while volume will increase. In order to keep the temperature constant, we have to supply required amount of heat from source to cylinder.Since in this expansion, temperature is constant therefore it is known as Isothermal Expansion.

ii. Isothermal CompressionIn this process, cylinder is placed on a sink and piston is allowed to move downward. When we do so temperature and pressure of working substance will increase while volume will decrease. In order to maintain the temperature, we have to reject required amount of heat from cylinder to the sink.Since in this compression, temperature is kept constant therefore it is known as isothermal compression.

SECOND LAW OF THERMODYNAMICS

IntroductionIt is inherit tendency of heat that it always flows from hot reservoir to cold reservoir. Rather than to flow in both the directions with equal probability. On the basis of this tendency of heat a law was proposed that is known as Second Law of Thermodynamics.

StatementIt is impossible to construct a process which reserves the natural tendency of heat.This law is also known as Law of heat and can also be stated asEfficiency of heat engine is always less than unity.

ExplanationMany statements of this law has been proposed to cover similar but different point of vies in which two are given below.1. Lord Kelvin Statement2. Clausius Statement

1. Lord Kelvin StatementAccording to this statement,It is impossible to construct a heat engine which extract all heat form the source and convert it into equal amount of work done and no heat is given to the sink.

Mathematically,Q1 ≠ WQ2 ≠ O

2. Clausius StatementAccording to Clausius Statement,Without the performance of external work heat cannot flow from cold reservoir towards, the hot reservoir.

ExampleIn case of refrigerator flow of heat is unnatural but this unnatural flow of heat is possible only when we apply electrical power on the pump of the refrigerator.

Qs. Define the term Entropy and Give its Uses

ENTROPY

Definition

It measures the disorderness of any system.

Mathematically,ΔS = ΔQ/TWhere Δs shows change in entropy.

UnitsJoule per degree Kelvin – J/°K.

ExplanationAs we know that incase of isometric process volume is constant. In case of Isothermal process temperature and pressure is constant, but in case of adiabatic process neither temperature, nor pressure or volume is constant but one thermal property is constant which is known as Entropy.There are two types of Entropy.1. Positive Entropy2. Negative Entropy

1. Positive EntropyIf heat is supplied to the system the entropy will be positive.

2. Negative EntropyWhen heat is rejected by the system the entropy will be negative.

Qs. What is carbot engine an carnot cycle?

CARNOT ENGINE

Definition

‘Carnot engine is an ideal heat engine which converts heat energy into mechanical energy.

Working of Carnot EngineIt consists of a cylinder and a piston. The walls of the cylinder are non-conducting while the bottom surface is the conducting one. The piston is also non-conducting and friction less. It works in four steps. Which are as follows.1. Isothermal Expansion2. Adiabatic Expansion3. Isothermal Compression4. Adiabatic Compression

1. Isothermal ExpansionFirst of all, cylinder is placed on a source and allow to move upward as a result temperature and pressure of the working substance decreases, while volume increases. In order to maintain temperature we have to supply more amount of heat from source to the cylinder. Since in this expansion temperature is kept constant.

2. Adiabatic ExpansionSecondly cylinder is placed on an insulator and piston is allow to move downward as a result temperature and pressure of working substance will decrease. While volume will increase but no heat is given or taken of the cylinder.

3. Isothermal CompressionIn this state cylinder is placed on a sink and piston is allow to move downward as a result temperature and pressure of the working substance will increase while volume will decrease. In order to maintain temperature we have to reject extra heat from cylinder to the sink. Since in this compression temperature is constant.

4. Adiabatic CompressionFinally cylinder is placed on an insulator and piston is a flow to move downward, when we do so neither temperature nor pressure or volume is constant. But no heat is given or taken out of the cylinder.

CARNOT CYCLE

Definition

By combining the four processess Isothermal Expansion, Adiabatic Expansion, Isothermal Compression and Adiabatic Compression which are carried out in carnot engine, then we get a cycle knows as Carnot cycle.

Qs. How can we increase the efficiency of Heat Engine?

If we want to increase the efficiency of any heat engine then for this purpose we have to increase temperature of source as maximum as possible and reduce the temperature of sink as minimum as possible.

Qs. Define Specific Heat and Molar Specific Heat.

SPECIFIC HEAT

Definition

Specific heat is the amount of heat required to raise the temperature of a unit mass of a substance by one degree centigrade.

Different substances have different specific heat because number of molecules in one kg is different in different substances. It is denoted by c.

Mathematical Expression

Consider a substance having mass m at the temperature t1. The amount of heat supplied is ΔQ, which raises the temperature to t2. The change in temperature is Δt.The quantity of heat is directly proportional to the mass of the substance.ΔQ ∞ mAnd the temperature differenceΔQ ∞ ΔtCombining both the equationsΔQ ∞ mΔt=> ΔQ = cmΔt=> c = ΔQ / mΔt —- (I)Where c is the specific heat of the substance. Its unit is Joules / Kg°C.

MOLAR SPECIFIC HEAT

Definition

Molar specific heat is the amount of heat required to raise the temperature of one mole of a substance through one degree celsius.

Almost all the substances have the same amount of molar specific heat because the numbers of molecules in all substances are same in one mole. It is denoted by cM.

Mathematical Expression

Mathematically,No. of Moles = Mass / Molecular Mass

=> n = m / M=> nM = m=> nM = ΔQ / nΔtWhere n is the number of moles. The unit of molar specific heat is J/Kg°C.

Qs. Define Molar Specific Heat at Constant volume and at Constant Pressure.

MOLAR SPECIFIC HEAT AT CONSTANT VOLUME

Definition

The amount of heat required to raise the temperature of one mole of any gas through one degree centigrade, at constant volume is known as molar specific heat volume.

It is denoted by Cv.

Mathematical Expression

Mathematically,ΔQv = nCvΔtWhere ΔQv is the heat supplied at constant volume.

MOLAR SPECIFIC HEAT AT CONSTANT PRESSURE

Definition

The amount of heat required to raise the temperature of unit mass of a substance through one degree centigrade at constant pressure is known as Molar Specific Heat at Constant Pressure.

It is denoted by Cp.

Mathematical Expression

Mathematically,ΔQp = nCpΔtWhere ΔQp is the heat supplied at constant volume.