## Wednesday, July 17, 2013

### Class XII, PHYSICS, Chapter # 11, "Heat"

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.
UNITS
Since 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 TEMPERATURE
There are three main scales of temperature.
1. Celsius Scale
2. Fahrenheit Scale
3. Kelvin Scale
Celsius and Fahrenheit scales are also known as Scales of Graduation.
1. Celsius Scale
The 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 – 273
OR
°C = 5/9 (°F – 32)
2. Fahrenheit Scale
The 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 Scale
The 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.
Explanation
If 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 Expansion
There are three types of Thermal Expansion.
1. Linear Expansion
2. Superficial Expansion
3. 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
CONSIDERATION
Let 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
Derivation
The 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 get
ΔL ∞ LoΔt
=> ΔL = ∞LoΔt
Where 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, then
Lt = Lo + ΔL
=> Lt = Lo + αLoΔt
=> Lt = Lo (1 + αΔt)
COEFFICIENT OF VOLUMETRIC EXPANSION
Consideration
Let 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
Derivation
The 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 = βVoΔt
Where β is the constant of proportionality and it is known as coefficient of Volumetric Expansion. It is defined as
It 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 then
Vt = Vo + ΔV
=> Vt = Vo + αβVo Δt
=> Vt = Vo (1 + βΔt)
State and Explain Boyle’s Law and Charle’s Law.
INTRODUCTION
Gas Laws are the laws, which give relationship between Pressure, Volume, temperature and mass of the gas. There are two gas laws.
1. Boyle’s Law
2. Charle’s Law
BOYLE’S LAW
Statement 1
According 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 Form
Mathematically,
V ∞ 1/P
=> V = K 1/P
=> PV = K (Constant)
P1V1 = P2V2 = … = K
=> P1V1 = P2V2
The above equation is mathematical form of Boyle’s Law.
Statement II
According 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 III
According 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 Form
Mathematically,
PV ∞ m
=> PV = Km
=> PV/m = K
=> P1V1/m1 = P2V2/m2
Limitations of Boyle’s Law
Boyle’s Law does not hold good at high pressure, because at high pressure gases convert into liquid or solid.
Graphical Representation
The 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 I
According 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 Form
Mathematically,
V ∞ T
=> V = KT
=> V/T = K
OR
=> V1/T1 = V2/T2
The above equation is mathematical form of Charles Law.
Statement II
According 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 Law
This 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 Law
V ∞ T —- (II)
V ∞ 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 that
R = R/NA
=> R = KNA
Where K is the Boltzman constant, Its value is
K = 1.38 x 10(-23) J/K
Substituting the value of R in eq (A)
=> PV = nKNAT
=> PV = nNAKT
But nNA = N1 (Total number of molecules), therefore,
PV = NtKT
=> P = Nt/V KT
Since Nt/V = N (Total Number of molecules in a given volume), therefore,
P = NKT
The above equation is other form of General Gas Equation.
Qs. What are the basic postulates of Kinetic Molecular Theory pf Gases?
INTRODUCTION
The 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. Composition
All gases are composed of small, spherical solid particle called molecules.
2. Dimension of Molecules
The dimensions of the molecules is compared to the separation between the molecule is very small.
3. Number of Molecules
At standard condition, there are 3 x 10(23) molecules in a cubic meter.
4. Pressure of Gas
Gas 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 Molecules
The collision between the molecules is elastic in which momentum and Kinetic energy remains constant.
7. Kinetic Energy of Molecules
If 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 Interraction
There is no force of attraction or repulsion between the molecules.
9. Law of Mechanics
Newtonian mechanics is applicable to the motion of molecules.
THERMODYNAMICS
DEFINITIONS
The 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 Thermodynamics
There are two laws of thermodynamics.
1. First Law of Thermodynamics
2. 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 Statement
Whenever 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 = JW
Where J is the mechanical equivalent of heat or joules constant. Its value is 4.2 joules.
Second Statement
If 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 Expression
Mathematically,
ΔQ – Au + Δw
The above equation is the mathematical form of first law of thermodynamics.
Where
Δu = 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 Statement
For 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 Expression
Mathematically,
Q(IN) + W(IN) = Q(OUT) + W(OUT)
Q(IN) – Q(OUT) = W(OUT) + W(IN)
ΔQ = ΔW
{dQ = {dW
{Shows cyclic process
Fourth Statement
For a system and surrounding the total amount of heat energy remains constant
APPLICATIONS OF THE LAW
There are four applications of first law of Thermodynamics.
1. Isometric or Isocohric Process.
2. Isobaric Process
3. Isothermal Process
1. Isometric or Isocohric Process
The 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 Form
In this process first law of thermodynamics take the following form.
ΔQ = Δu + ΔW
But,
ΔW = 0
=> ΔQ = Δu = 0
=> ΔQ = Δu
2. Isobaric Process
The 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 Process
A process in which temperature is kept constant is known as Isothermal Process.
There are two parts of isothermal process.
i. Isothermal Expansion
ii. Isothermal Compression
i. Isothermal Expansion
In 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 Compression
In 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
Introduction
It 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.
Statement
It 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 as
Efficiency of heat engine is always less than unity.
Explanation
Many statements of this law has been proposed to cover similar but different point of vies in which two are given below.
1. Lord Kelvin Statement
2. Clausius Statement
1. Lord Kelvin Statement
According 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 ≠ W
Q2 ≠ O
2. Clausius Statement
According to Clausius Statement,
Without the performance of external work heat cannot flow from cold reservoir towards, the hot reservoir.
Example
In 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/T
Where Δs shows change in entropy.
Units
Joule per degree Kelvin – J/°K.
Explanation
As 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 Entropy
2. Negative Entropy
1. Positive Entropy
If heat is supplied to the system the entropy will be positive.
2. Negative Entropy
When 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 Engine
It 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 Expansion
3. Isothermal Compression
1. Isothermal Expansion
First 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.
Secondly 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 Compression
In 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.
Finally 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 ∞ m
And the temperature difference
ΔQ ∞ Δt
Combining both the equations
ΔQ ∞ 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 / nΔt
Where 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 = nCvΔt
Where 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 = nCpΔt
Where ΔQp is the heat supplied at constant volume.