ENTROPY

 History 

The concept of entropy was introduced into the study of thermodynamics by Rudolph Clausius in 1856 to give a quantitative basis for the second law. 

State Variable 

It provides another variable to describe the state of a system to go along with pressure, volume, temperature and internal energy. If a system undergoes a reversible process during which it absorbs a quantity of heat ∆Q at absolute temperature T, then the increase in the state variable called entropy S of the system is given by 

Like potential energy or intemal energy, it is the change in entropy of the system which is important.

Positive Entropy 

Change in entropy is positive when heat is added and negative when heat is removed from the system. 

Explaination 

Suppose, an amount of heat Q flows from a reservoir at temperature T1 through a conducting rod to a reservoir at temperature T2 when T1 > T2. The change in entropy of the reservoir, at temperature T1, which loses heat, decreases by Q/T1 and of the reservoir at temperature T2, which gains heat, increases by Q/T2. 

As T1 > T2 so Q/T2 will be greater than Q/T1

i.e.

Q/T2 > Q/T1 

Hence, 

Net change in entropy = Q/T2 - Q/T1 is positive

Another statement of 2nd law of thermodynamics 

In all natural processes where heat flows from one system to another, there is always a net increase in entropy. This is another statement of 2nd law of thermodynamics. According to this law 

Statement:

"If a system undergoes a natural process, it will go in the direction that causes the entropy of the system plus the environment to increase."

Relation between entropy and molecular disorder

It is observed that a natural process tends to proceed towards a state of greater disorder. Thus, there is a relation between entropy and molecular disorder. 

For example: An irreversible heat flow from a hot to a cold substance of a system increases disorder because the molecules are initially sorted out in hotter and cooler regions. This order is lost when the system comes to thermal equilibrium. Addition of heat to a system increases its disorder because of increase in average molecular speeds and therefore, the randomness of molecular motion. 

Similarly, free expansion of gas increases its disorder because the molecules have greater randomness of position after expansion than before. Thus in both examples, entropy is said to be increased.

Conclusion 

We can conclude that only those processes are probable for which entropy of the system increases or remains constant. The process for which entropy remains constant is a reversible process; whereas for all irreversible processes, entropy of the system increases.

Entropy and work done 

Every time entropy increases, the opportunity to convert some heat into work is lost. For example there is an increase in entropy when hot and cold waters are mixed. Then warm water which results cannot be separated into a hot layer and a cold layer. There has been no loss of energy but some of the energy is no longer available for conversion into work. 

Therefore, increase in entropy means degradation of energy from a higher level where more work can be extracted to a lower level at which less or no useful work can be done. The energy in a sense is degraded, going from more orderly form to less orderly form, eventually ending up as thermal energy.

In all real processes where heat transfer occurs, the energy available for doing useful work decreases. In other words the entropy increases. Even if the temperature of some system decreases, thereby decreasing the entropy, it is at the expense of net increase in entropy for some other system. When all the systems are taken together as the universe, the entropy of the universe always increases.

POLARIZATION

 In transverse mechanical waves, such as produced in a stretched string, the vibrations of the particles of the medium are perpendicular to the direction of propagation of the waves The vibration can be oriented along vertical, horizontal or any other direction. In each of these cases, the transverse mechanical wave is said to be polarized. 

Plane Polarization 

The plane of polarization is the plane containing the direction of vibration of the particles of the medium and the direction of propagation of the wave. 

Unpolarized Light Waves 

A light wave produced by oscillating charge consists of a periodic variation of electric field vector accompanied by themagnetic field vector at right angle to each other Ordinary light has components of vibration in all possible planes. Such a light is unpolarized. 

Polarized Light Waves 

If the vibrations are confined only in one plane, the light is said to be polarized. 

Production and Detection of Plane Polarized Light

The light emitted by an ordinary incandescent bulb (and also by the Sun) is unpolarized, because its (electrical) vibrations are randomly oriented in space. It is possible to obtain plane polarized beam of light from un-polarized light by removing all waves from the beam except those having vibrations along one particular direction. 

Methods of Polarization 

Polarization can be achieved by various processes such as 

1. selective absorption 
2. reflection from different surfaces
3. refraction through crystals
4. scattering by small particles. 

The selective absorption method is the most common method to obtain plane polarized light by using certain types of materials called dichroic substances. 

Polaroid

The materials transmit only those waves, whose vibrations are parallel to a particular direction and will absorb those waves whose vibrations are in other directions. One such commercial polarizing material is a polaroid.

Experiment to prove that light waves are transverse in nature

1. If un-polarized light is made incident on a sheet of polaroid.
2. The transmitted light will be plane polarized.
3. If a second sheet of polaroid is placed in such a way that the axes of the polaroids, shown by straight lines drawn on them, are parallel, the light is transmitted through the second polaroid also.
4. If the second polaroid is slowly rotated about the beam of light, as axis of rotation, the light emerging out of the second polaroid gets dimmer and dimmer and disappears when the axes become mutually perpendicular.
5. The light reappears on further rotation and becomes brightest when the axes are again parallel to each other. 

Result 

This experiment proves that light waves are transverse waves. If the light waves were longitudinal, they would never disappear even if the two polaroids were mutually perpendicular

Reflection from different surfaces 

Reflection of light from water, glass, snow and rough road surfaces, for larger angles of incidences, produces glare. Since the reflected light is partially polarized, glare can considerably be reduced by using polaroid sunglasses. 

Reflection by small particles 

Sunlight also becomes partially polorized because of scattering by air molecules of the Earth's atmosphere. This effect can be observed by looking directly up through a pair of sunglasses made of polarizing glass. At certain orientations of the lenses, less light passes through than at others.

Optical Rotation

When a plane polarized light is passed through certain crystals, they rotate the plane of polarization. Quartz and sodium chlorate crystals are typical examples, which are termed as optically active crystals. 

Refraction through crystals

A few millimeter thickness of such crystals will rotate the plane of polarization by many degrees. Certain organic substances, such as sugar and tartaric acid, show optical rotation when they are in solution. This property of optically active substances can be used to determine their concentration in the solutions.

What are Dimensions ?

 Each base quantity is considered a dimension denoted by a specific symbol written within square brackets. 

It stands for the qualitative nature of the physical quantity. For example, different quantities such as length, breadth, diameter, light year which are measured in metre denote the same dimension and has the dimension of length [L]. Similarly the mass and time dimensions are denoted by [M] and [T ] respectively. 

Other quantities that we measure have dimension which are combinations of these dimensions. For example. speed is measured in meter per second. This will obviously have the dimensions of length divided by time. Hence we can write ✍️

Dimensions of speed = [L]/[T]

Similarly  the dimensions of acceleration are = [L]/[T2]

And that of force = [M][L]/[T2]

Using the method of dimensions called the dimensional analysis we can check the correctness of a given formula for an equation and can also derive it. 

Assessment of total uncertainty in the final result

 

To assess the total uncertainty or error, it is necessary to evaluate the likely uncertainties in all the factors involved in that calculation. The maximum possible uncertainty or error in the final result can be found as follows. 

1. For addition and subtraction 

Absolute uncertainties are added: 

For example, the distance x determined by the difference between two separate position measurements x1=10.5±0.1 cm  and x2 = 26.8 1±0.1 cm is recorded as

x=x2 - x1=16.3±0.2 cm.

2. For multiplication and division 

Percentage uncertainties are added. 

For example the maximum possible uncertainty in the value of resistance R of a conductor determined from the measurements of potential difference V and resulting current flow I by using

R = V/I is found as follows: 

V=5.2±0.1 V

I = 0.84±0.05A

The %age uncertainty for V is = 0.1V/5.2V × 100 = about 2%

The %age uncertainty for I is = 0.05A/0.84A × 100 = about 6%

Hence total uncertainty in the value of resistance R when V is divided by I is 8%. The result is thus quoted as 

R = 5.2V/0.84A = 6.19 V/A = 6.19 ohms with a % age uncertainty of 8%

that is R = 6.2 1±0.5 ohms.

The result is rounded off to two significant digits because both V and R have two significant figures and uncertainty, being an estimate only, is recorded by one significant figure.

4. For power factor

Multiply the percentage uncertainty by that power. 

For example, in the calculation of the volume of a sphere using

V = 4/3 π r³

%age uncertaintyin V= 3 x %age uncertainty in radius r.

As uncertainty is multiplied by power factor, it increases the precision demand of measurement. If the radius of a small sphere is measured as 2.25 cm by a vernier callipers with least count 0.01 cm, then the radius r is recorded as

r= 2.25±0.01 cm 

Absolute uncertainty = Least count = 0.01 cm

%age uncertainty in r= 0.01 cm / 2.25 cm ×100 = 0.4% 

Total percentage uncertainty in V = 3 × 0.4 = 1.2%

Thus volume  V= 4/3π r³

            = 4/3 × 3.14 × ( 2.25 cm)3

            = 47.689 (cm)3

 with 1.2% uncertainty

Thus the result should be recorded as

V = 47.71 (+0.6 or -0.6) cm3

4. For uncertainty in the average value of many measurements.

(i) Find the average value of measured values.

(ii) Find deviation of each measured value from the average value.

(iii) The mean deviation is the uncertainty in the average value. 

For example, the six readings of the micrometer screw gauge to measure the diameter of a wire in mm are:

1.20, 1.22, 1.23, 1.19, 1.22, 1.21 

Then Average:

             =(1.20+1.22+1.23+1.19+1.22+1.21)/6

         = 1.21 mm

The deviation of the readings, which are the difference without regards to the sign, between each reading and average value are 0.01, 0.01,-0.02, 0.02, 0.01, 0. 

Mean of deviations = (0.01 +0.01 +0.026+0.02 +0.01+ 0)/6 

                                    = 0.01 mm 

Thus, likely uncertainty in the mean diametre 1.21 mm is 0.01 mm recorded as 1.21±0.01 mm.

5. For the uncertainty in a timing experiment 

The uncertainty in the time period of a vibrating body is found by dividing the least count of timing device by the number of vibrations. 

For example, the time of 30 vibrations of a simple pendulum recorded by a stopwatch accurate upto one tenth of a second is 54.6 s, the period 

T = 54.6 s / 30 = 1.82 s with uncertainty 0.1/30 = 0.003 s

Thus, period T is quoted as T = 1.82±0.003 s.

Hence, it is advisable to count large number of swings to reduce timing uncertainty.

What is precision and accuracy?

 

In measurements made in physics, the terms precision and accuracy are frequently used. They should be distinguished clearly. 

The precision of a measurement is determined by the instrument or device being used and the accuracy of a measurement depends on the fractional or percentage uncertainty in that measurement.

For example:

When the length of an object is recorded as 25.5 cm by using a metre rod having smallest division in millimetre, it is the difference of two readings of the initial and final positions. The uncertainty in the single reading as discussed before is taken as 0.05 cm which is now doubled and is called absolute uncertainty equal to ±0.1 cm. Absolute uncertainty, in fact, is equal to the least-count of the measuring instrument.

Precision or absolute uncertainty = ±0.1 cm

Fractional uncertainty = 0.1cm/25.5cm = 0.004

Percentage uncertainty = 0.1cm/25.5cm × 100 = 0.4%

Another measurement taken by vernier callipers with least count as 0.01 cm is recorded as 0.45 cm. it has Precision or absolute uncertainty (least count) = ±0.01 cm

Fractional uncertainty = 0.01cm/0.45 = 0.02

Percentage uncertainty = 0.01cm/0.45 = 2%

Thus the reading 25.5 cm taken by meter rule is although less precise but is more accurate having less percentage uncertainty or error.

Whereas the reading 0.45 cm taken by vernier callipers is more precise but is less accurate. In fact, it is the relative measurement which is important. The smaller a physical quantity, the more precise instrument should be used. Here the measurement 0.45 cm demands that at more precise instrument, such as micrometre screw gauge, with least count 0.001 cm, should have been used. Hence, we can conclude that:

A precise measurement is one which has less absolute uncertainty and an accurate measurement is one which has less fractional or percentage uncertainty or error.

Significant Figures

 

In any measurement, the accurately known digits and first doubtful digit are known as significant figures.

we must know the following rules in deciding how many significant figures are to be retained in the final result. 

     1. All digits 1,2,3,4,5,6,7,8,9 are significant. 

However, zeros may or may not be significant. ln case of zeros, the following rules may be adopted.

• A zero between two significant figures is itself significant.
• Zeros to the left of significant figures are not significant. For example, none of the zeros in 0.00467 or 02.59 is significant.
• Zeros to the right of a significant figure, may or may not be significant. In decimal fraction, zeros to the right of a significant figure are significant. For example, all the zeros in 3.570 or 7.4000 are significant.

However, in integers such as 8,000 kg, the number of significant zeros is determined by the accuracy of the measuring instrument. If the measuring scale has a least count of 1 kg then there are four significant figures written in scientific notation as 8.000 x 10^3 kg. 

If the least count of the scale is 10 kg, then the number of significant figures will be 3 written in scientific notation as 8.00 x 10^3 kg and so on.

• When a measurement is recorded in scientific notation or standard form, the figures other than the powers of ten are significant figures. For example, a measurement recorded as 8.70 x 10^4 kg has three significant figures.

       2. In multiplying or dividing numbers, keep a number of significant figures in the product or quotient not more than that contained in the least accurate factor i.e., the factor containing the least number of significant figures. 

                    For example, the computation of the following using a calculator gives 

    

    5.348×10^-2×3.64×10^4  = 1.45768982×10^2

                   1.336  

As the factor 3.64 x 10^4 the least accurate in the above calculation has three significant figures, the answer should be written to three significant figures only. The other figures are insignificant and should be deleted. 

While deleting the figures, the last significant figure to be retained is rounded off for which the following rules are followed.

a) If the first digit dropped is less than 5, the last digit retained should remain unchanged.

b) If the first digit dropped is more than 5, the digit to be retained is increased by one.

c) If the digit to be dropped is 5, the previous digit which is to be retained, is increased by one if it is odd and retained as such if it is even. For example, the following numbers are rounded off to three significant figures as follows. The digits are deleted one by one.

43.75 is rounded off as 43.8

56.8546 is rounded off as 56.8

73.650 is rounded-off as 73.6

64.350 is rounded off as 64.4

               3. In adding or subtracting numbers, the number of decimal places retained in the answer should equal the smallest number of decimal places in any of the quantities being added or subtracted. 

In this case, the number of significant figures is not important. It is the position of decimal that matters. For example, suppose we wish to add the following quantities expressed in metres. 

                i) 72.1                      ii) 2.7543

               +   3.42                    +        4.10

               +  0.003                 +       1.2737

                  5.523                           8.1273

Correct answer:     75.5 m        8.13 m

In case (i) the number 72.1 has the smallest number of decimal places, thus the answer is rounded off to the same position which is then 75.5 m. In case (ii) the number 4.10 has the smallestnumberof decimal places and hence the answer is rounded off to the same decimal positions which is then 8.13m.

Errors and Uncertainties

 

All physical measurements are uncertain or imprecise to some extent. 

It is very difficult to eliminate all possible errors or uncertainties in a measurement.

 The error may occur due to» 

1. negligence or inexperience of a person
2. the faulty apparatus
3. inappropriate method or technique.

Uncertainty:

                       The uncertainty may occur due to inadequacy or limitation of an instrument, natural variations of the object being measured or natural imperfections of a person's senses.

However, the uncertainty is also usually described as an error in a measurement. 

There are two major types of errors.

1. Random error
2. Systemic error

Random error is said to occur when repeated measurements of the quantity, give different values under the same conditions. It is due to some unknown causes. 

How to reduce Random? Repeating the measurement several times and taking an average can reduce then effect of random errors.

Systematic error refers to an effect that influences all measurements of a particular quantity equally. It produces a consistent difference in readings. It occurs to some definite rule. It may occur due to zero error of instruments, poor calibration of instruments or incorrect markings etc. 

Systematic error can be reduced by comparing the instruments with another which is known to be more accurate. Thus for systematic error, a correction factor can be applied.

International system of units

The eleventh General Conference on Weight and Measures held in Paris in 1960 adopted a world-wide system of measurements called International System of Units. The International System of Units is commonly referred as SI.

The system international consists of seven base units and two supplementary units that are given below:

Base Units

1. Meter 
2. Second
   
3. Kilogram
4. Candela
5. Ampere
6. Kelvin
7. Mole

Supplementary Units

• Radian
• Steradian

1. Meter 

                One meter is the unit of length and it is defined as: the distance covered by light in vacuum during a time interval of 1/299,792,458 of a second.

2. Second

                One second is defined as “9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom”. 

3. Kilogram 

                The kilogram is the unit of mass. It is defined as the mass of a particular international prototype (نمونہ) made of platinum-iridium and kept at the International Bureau of Weights and Measures.

4. Candela

                The candela is the SI unit of luminous intensity. The candela is used to measure the visual intensity of light sources, like light bulbs or the bulbs in torches. It is the only SI base unit based on human perception.

5. Ampere

                   The ampere is a measure of the amount of electric charge in motion per unit time.

6. Kelvin

                  One kelvin is formally defined as 1/273.16 of the thermodynamic temperature of the triple point of pure water. 

(Triple point: the condition of temperature and pressure under which the gaseous, liquid, and solid phases of a substance can exist in equilibrium)

7. Mole.    

       A mole is defined as 6.02214076×10²³ of some chemical unit, be it atoms, molecules, ions, or others. The mole is a convenient unit to use because of the great number of atoms, molecules, or others in any substance.

* Radian

                 One radian is the angle subtended at the centre of. a circle by an arc equal in length to the radius of. the circle. 

* Steradian

                 The solid angle subtended at the centre of a sphere, by that surface of the sphere, which is equal in area, to the square of radius of the sphere.

What are Physical quantities ?

All measure able quantities are known as physical quantities, such as length 🦯, time 🕒, mass, temperature 🌡️ etc.

Each physical quantity has at least two characteristics:

• Numerical Magnitude
• Unit of measurement

For Example: A student measure the height of another student 150 cm. In this measurement "150" is numerical Magnitude while "cm" is unit of measurement.

                                                                                  

Physical quantities are divided into two streams:

1. Base Quantities
2. Derived Quantities

Base quantities

                             The quantities on the basis of which other Quantities are expressed are known as base quantities, these includes length, time, mass, electric current, intensity of light, temperature and amount of substance.

Derived quantities 

                                    The quantities that are expressed on the basis of base quantities are known as derived quantities, such as velocity, acceleration, force, momentum and energy etc.

What is physics?

 

Physics is the branch of science in wich we study about matter, energy and their mutual relationship.

In physics we study about matter (anything that has some sort of weight and cover some place) that includes solid, liquid, gas and plasma. 

In case of matter we study about motion of objects, its causes and effects.

There are some branches of Physics that study the matter, are given below 👇

• Mechanics (kinematics and dynamics)
• Solid state physics
• Atomic physics
• Particle physics
• Rotational physics
• Fluid dynamic

In physics we study about energy (capable to do work) that includes Heat Radiations and Light.

There are some branches of Physics that study the energy, are given below 👇

• Thermodynamics
• Sound
• Work
• Photonics
• Light

Matter and energy are enter convertible. 

According to Einstein "mass is the most concentrated form of energy."  

What is Science?

 Science is the knowledge that gained through observations and experimentations.

This knowledge is based on five processes that are,

1. Observation
2. Hypothesis
3. Experiment
4. Theory
5. Law

1. Observation 

                             Observations are made by five human senses. Human (scientist) firstly observe the natural phenomena and think how is it happening. This thinking comes out as scientific discovery.

2. Hypothesis

                           After observation the human (scientist) make a hypothesis in his mind that this natural phenomena is happening on these principles, without any experiment.

3. Experiment

                          A scientist perform an experiment for proving his hypothesis true or false. In doing so he comes to know the actual natural phenomena of an scientific process or may be he discovered some new scientific phenomenas.

4. Theory

                       The results of an experiment become scientific theory. Every scientist can do same experiment and observe the results of that experiment, again and again. He may modify some aspects.

5. Law

                      A scientific theory becomes Law, if no scientist could prove it wrong, in next 200 years.