# Thermal Physics [ 4 Topics ]

Thermal Physics deals with material properties and events related to heat such as thermal expansion, heat capacity, latent heat, change of state, heat transfer, etc. Class 11th Thermal Physics is given due importance in the NCERT syllabus.

NCERT assigns 20 marks questions based on Thermal Physics plus Elasticity and Fluid Mechanics out of 70 marks in the Class 11 CBSE physics exam paper (theory).

Recent IIT-JEE Main and NEET papers assign more than 10% weightage to Thermal Physics. A student of class 11th and 12th under CBSE, ISC, or any other provincial Board, if you aspire to succeed in competitive examinations like IIT-JEE or NEET, you will learn everything that you needed from our class 11 Thermal Physics videos lectures.

The lectures lucidly explain the basic theories in detail and solve a large number of graded problems – from simple to advanced – to improve your problem-solving skill. Our lectures will be extremely useful to any student preparing for any Physics-based Board or competitive exams anywhere in the world.

The topics which come under Class 11th Thermal Physics as per the latest syllabus are as follows:"

Unit I : Properties of Bulk Matter (Continued)

• Chapter 1: Thermal Properties of Matter

Unit II : Thermodynamics
• Chapter 2: Laws of Thermodynamics

Unit III : Behaviour of Perfect Gases and Kinetic Theory of Gases
• Chapter 3: Kinetic Theory

1. #### Thermal Expansion 18 Videos

In general, all bodies expand when they are heated and contract when cooled. The expansion or contraction, as the case may be, is small in solids, larger in liquids, and the largest in gases. The increase in length, width or height of a solid is called linear expansion. The increase in area is called surface expansion. The increase in volume is called volume expansion or cubical expansion. A liquid or a gas has only volume expansion.

Suppose the length of a rod increases from an initial value of l1 at temperature θ1 to a final value of l2 at higher temperature θ2. The relation between these two lengths is:

l2 = l1 [1 + α (θ2 - θ1)]

Here α is a constant of proportionality, known as the coefficient of linear expansion for the solid material of the rod. The dimension of α is [K-1] , and its unit is per kelvin (/K).

In a similar way, we can relate the surface areas of a solid plate at two different temperatures as:

S2 = S1 [1 + β (θ2 - θ1)]

where β is the coefficient of surface expansion for the solid. And for change in volume with temperature:

V2 = V1 [1 + γ(θ2 - θ1)]

The quantity, γ, is the coefficient of volume expansion. All these three coefficients have the same dimension and the same unit. And for an isotropic solid, a simple relation exists among them:

α = β/2 = γ/3

Thus, referring to one table for the values of α of various solids, we can determine the corresponding values of β and γ.

Some notable effects of thermal expansion of solids are expansion of a measuring scale, a faulty pendulum clock that runs slow in summer, thermal stress experienced by a rod fixed between two rigid walls, deformation of a bimetallic strip that is cleverly used in a thermostat to switch an air-conditioner on and off.

While discussing the expansion of liquids, it must be kept in mind that both the liquid and the solid container expand in volume as temperature goes up. So it is important to distinguish between apparent expansion and real expansion of a liquid. Correspondingly, there would be two coefficients for a liquid: coefficient of apparent expansion and coefficient of real expansion. The relation between these two coefficients is:

γr = γa + γg

The symbols are nearly self-explanatory; γg is the coefficient of volume expansion of glass or any other solid material from which the container is made. The coefficients of real expansion of liquids are significantly greater than the coefficients of volume expansion of solids.

Some devices to measure the coefficients of expansion of a liquid are dilatometer or volume thermometer, weight thermometer, Dulong and Petit's apparatus etc.

One notable effect of thermal expansion of liquids is the change in buoyant force on an immersed body with change in temperature. Another is the correction factor to be introduced to the reading of a barometer if the ambient temperature is different from the temperature of calibration. Anomalous expansion of water refers to the strange phenomenon of water contracting in volume as its temperature rises from 0°C to 4°C, implying a negative expansion coefficient in that range!

Expansion of gases is dictated by three famous laws: Boyle's law, Charles' law and pressure law. The last two laws lead us to the concept of absolute zero of temperature, which is - 273.15°C or 0 K. This is the temperature at which, theoretically, a gas would occupy zero volume and exert zero pressure. In reality, all gases change into liquid phase much above absolute zero. Combining Boyle's law and Charles' law, we can arrive at the equation of state of an ideal gas which is:

PV = nRT

Here P is pressure and V is volume of n moles of gas at Kelvin temperature T. The quantity R is called universal gas constant, because its value is the same 8.31 J/mol-K for all gases. The ratio of universal gas constant and Avogadro's number is called Boltzmann's constant. The equation of state of a gas mixture can be derived by making use of Dalton's law of partial pressure.

2. #### Calorimetry And Change Of Phase 14 Videos

Heat is defined as the thermal energy that flows from a system to its surroundings or the other way round solely as a result of the difference between their temperatures. The flow always takes place from a higher temperature to a lower temperature, and never in the reverse direction. The CGS unit of heat is calorie (cal); a larger unit kilocalorie is also used. Since heat is now recognised as a form of energy, CGPM insists that we use the SI unit of energy, joule (J), as the unit of heat. 1 cal = 4.186 J.

The specific heat capacity, or simply specific heat, of a substance is defined as the amount of heat required to raise the temperature of unit mass by one degree. Its SI unit is J/kg-K. If Q is the heat supplied to raise temperature of a body of mass m and specific heat capacity c from θ1 to θ2 then:

Q = cm (θ2 - θ1)

The molar heat capacity or molar specific heat of a substance is defined as the amount of heat required to raise the temperature of one mole of the substance by one degree. Its SI unit is J/mol-K. If Q is the heat required to raise temperature of n moles of a substance of molar heat capacity C from θ1 to θ2 then:

Q = Cn (θ2 - θ1)

The heat capacity of a body is defined as the amount of heat required to raise its temperature by one degree. Its SI unit is J/K. Once you distinguish heat capacity from molar heat capacity and specific heat capacity, you should be able to deduce the relation between any two of them.

The water equivalent of a body is the mass of water which has the same heat capacity as the body itself.

When a hot body is brought into contact with comparatively cold surroundings, heat flows from the body to the surroundings until their temperatures become equal. The experiments of calorimetry are usually carried out inside a properly insulated metal vessel known as a calorimeter. The hot body placed in the vessel is the "system"; the calorimeter and calorimetric liquid together are the "surroundings". Assuming no heat enters or exits the calorimeter and no chemical reaction takes place inside it:

Heat lost by hotter system = heat gained by colder surroundings

This is the fundamental principle of calorimetry.

The term phase means the state in which a substance exists, i.e. solid, liquid or gas. For example, the chemical substance H2O exists as ice in the solid phase, water in the liquid phase and water vapour or steam in the gas phase.

When a substance changes phase, the process does not take place abruptly. It happens at a constant temperature, even though heat is either supplied to or withdrawn from the system. The amount of heat required to change the phase of unit mass of a substance is known as the latent heat, L, of the substance. If Q is the amount of heat required to change the phase of mass m of a substance then:

Q = mL

The SI unit of latent heat is J/kg. If the phase changes from solid to liquid, we use the term latent heat of fusion. If the change happens from liquid to gas, the term used is latent heat of vaporisation. There are standard calorimetric experiments to determine latent heat of fusion of ice and latent heat of vaporisation of water. The first one is 3.33 x 105 J/kg, while the latter is 2.26 x 106 J/kg.

The equivalence between mechanical work and heat was established in the 19th century chiefly through the efforts of Robert Mayer and Helmholtz in Germany and James Joule in England. If W is the mechanical work which produces the same rise in temperature of a system as does the flow of heat Q then:

W = JQ

The quantity J is a constant of proportionality known as the mechanical equivalent of heat. The best modern value of J is 4.186 J/cal.

Let us touch upon various types of phase change. The change of phase from solid to liquid is called fusion or melting. The reverse process in which a substance changes from liquid to solid phase is called freezing or solidification. The temperature at which melting takes place under a pressure of 1 atm is called the normal melting point of the substance. The temperature at which freezing takes place under 1 atm pressure is called the normal freezing point of the substance. For a crystalline substance, these two temperatures are usually the same.

The change of phase from liquid to vapour is called vaporisation. The reverse process in which a substance changes from vapour to liquid is called condensation. Vaporisation can take place in two ways: evaporation and boiling. Evaporation is a slow process which happens at any temperature from the surface of a liquid. Shallow ponds dry up in summer due to evaporation. Boiling is a rapid, vigourous process that takes place throughout the mass of the liquid. The temperature at which boiling takes place under a pressure of 1 atm is called the normal boiling point of the substance.

Substances like iodine, camphor and naphthalene change directly from solid to vapour phase on heating. This type of phase change is called sublimation. The amount of heat absorbed by unit mass of a substance to sublimate is called the latent heat of sublimation.

3. #### Kinetic Theory Of Gases, And Properties Of Vapour 20 Videos

The experiments of James Joule during the 1840s proved beyond doubt that mechanical work and heat are equivalent. They also delivered the final blow to the erstwhile caloric theory of heat. The collapse of caloric theory inspired three gentlemen — Rudolf Clausius, Clerk Maxwell and Ludwig Boltzmann — to develop the kinetic theory of gases from a theoretical standpoint. The experimental proof of kinetic theory came a few decades later, in 1909, chiefly through the investigation of Brownian motion by Albert Einstein and Jean Perrin. Although originally developed for gases, kinetic theory can be extended to explain the thermal phenomena in solids and liquids.

The total energy of a system usually consists of external energy and internal energy. External energy is made up of potential energy due to an external conservative force and kinetic energy due to the motion of the system as a whole relative to its surroundings. Internal energy is made up of intermolecular potential energy, energy of molecular motion relative to the centre of mass of the system, and intramolecular energy. The energy of molecular motion (which can be translation, rotation and vibration) is the disordered part of internal energy and known as thermal energy. Even though it is impossible to determine how much internal energy a system possesses, we are interested only in the change in internal energy between two states and there are alternative methods to determine that.

The kinetic model of an ideal gas proposes a microscopic model in which any pure gas is made up of a large number of identical minute particles called "molecules". The molecules move randomly in the container in any direction at any speed between zero and infinity. As they move, molecules collide with one another and with the walls of the container. These collisions are all perfectly elastic and of negligible duration compared to the time spent between two successive collisions.

Using the kinetic model, the pressure exerted by an ideal gas is:

P = Mvrms2 / 3V = ρvrms2 / 3

where ρ is the density of the gas and vrms is the root mean square speed or RMS speed of the molecules of the gas. It follows that RMS speed can be expressed as:

vrms = √(3 RT / M0)

where M0 is the molar mass and T is the Kelvin temperature of the gas; R is the universal gas constant. Typically, the RMS speeds of hydrogen and oxygen gas molecules are 1836 m/s and 461 m/s respectively at 0°C.

It must be clearly understood that all molecules of a gas do not move with RMS speed. Many of the molecules move at speeds higher than RMS speed, while many others move at lower speeds. The distribution of molecular speeds is governed by a complex equation known as Maxwell distribution function. In fact, three different speeds are associated with Maxwell speed distribution curve. They are RMS speed, average speed and most probable speed. vrms > vav > vmp

The distance travelled by a molecule between two successive collisions is known as the free path and the average value of this quantity is called mean free path. The number of collisions taking place per unit time is called collision frequency. The reciprocal of collision frequency is called mean free time.

A gas which obeys the equation of state, PV = nRT, in all circumstances is known as an ideal gas. Strictly speaking, no real gas obeys the equation of state. But helium, hydrogen, nitrogen and oxygen which have extremely low boiling points behave like an ideal gas at room temperature and low pressure. Among several modified equations proposed for real gases, the best known is van der Waals' equation:

(P + n2a /V2)(V - nb) = nRT

In the expression, P, V and T have usual meanings; n is number of moles of the gas; a and b are positive constants characteristic of the gas.

When a space contains the maximum amount of vapour it can hold at a given temperature, the vapour is said to be saturated vapour. A vapour whose concentration is less than the maximum possible is said to be unsaturated vapour. The saturation vapour pressure (s.v.p. in short) of a liquid is the maximum pressure exerted by its vapour at a given temperature. In this context, two types of phase diagram are discussed: pressure-temperature phase diagram and pressure-volume phase diagram. Terms such as critical point and triple point are also introduced.

Because of continuous evaporation from the seas, rivers, moist earth etc, the atmosphere always contains varying amounts of water vapour. Hygrometry deals with the measurement of the amount of water vapour in a given volume of air. If air is gradually cooled to a temperature at which the s.v.p. of water is just equal to the actual pressure of water vapour, that temperature is called the dew point. If the temperature of air falls below the dew point, some vapour condenses and appears as tiny drops of water, which we call dew. The dew point varies with location and time.

The absolute humidity is defined as the mass of water vapour present per unit volume of air. A more useful term is relative humidity, which is the ratio of the mass of water vapour present in a given volume of air to the mass of water vapour required to saturate the volume. Regnault's hygrometer is a useful device to measure the relative humidity of air.

4. #### Laws of Thermodynamics 26 Videos

Thermodynamics is the branch of science which deals with the interconversion of heat and mechanical work, and the change in the properties of a system as it gains or loses energy in either form. Thermodynamics is mainly based on two empirical laws. Two system properties — internal energy and enthalpy — are associated with the first law. Another property called entropy is established as a consequence of the second law.

If a system is such that only heat can flow and work can be performed across its boundary but no matter can pass across, the system is called a thermodynamic system. The surroundings of a thermodynamic system are all other systems with which it can exchange energy. The thermodynamic properties are those characteristics of a system which describe its state. Thus, for a given amount of the gas, temperature (T), volume (V) and pressure (P) are its three thermodynamic properties. When a system simultaneously satisfies all the conditions necessary for thermal, mechanical and chemical equilibrium, no change is observed in the thermodynamic properties with time and the system is said to be in thermodynamic equilibrium. The path comprising a series of states through which the system passes to move from the initial state to the final state is called a process. If a system goes through a number of processes to eventually return to its initial state, we say that the system has gone through a cycle.

The Clausius statement of the first law of thermodynamics is:

The total energy of an isolated system remains constant whatever changes may occur within it. In mathematical terms:

Q = Δ U + W

where Q is the heat given to or withdrawn from the system, W is the work done by or on the system and ΔU is the change in internal energy of the system. All these three quantities may have positive or negative values depending on different possibilities.

A quasi-static process is one in which the properties of a system change so slowly that the deviation from thermodynamic equilibrium is infinitesimal. That is, each intermediate state through which the system passes during the process may be approximated as an equilibrium state. A quasi-static process can be plotted on a P-V, T-V or T-P diagram, while a non-quasistatic process can't be plotted.

Among the different types of molar heat capacity of an ideal gas, the molar heat capacity at constant volume, CV, and the molar heat capacity at constant pressure, CP, are of practical use. If QV is the heat required to raise temperature of n moles of a gas through ΔT at constant volume then:

QV = nCV ΔT

Similarly, if QP is the heat required to raise temperature of n moles of a gas through ΔT at constant pressure then:

QP = nCP ΔT

The relationship between these two molar heat capacities is given by Mayer's equation, which is:

CP = CV + R

Heat capacity ratio, γ, is the ratio of molar heat capacities of an ideal gas. That is:

γ = CP/CV

Kinetic theory of gases correctly predicts that, for monatomic gases, CV = 3R /2, CP = 5R /2, γ = 1.67; for diatomic gases, CV = 5R /2, CP = 7R /2, γ = 1.40; for polyatomic gases, CV = 3R, CP = 4R, γ = 1.33.

There are various types of quasi-static thermodynamic process, depending on which quantity remains constant and which quantities vary during the process. In an isothermal process, temperature remains constant while pressure and volume vary. In an isochoric process, volume remains constant while temperature and pressure very. In an isobaric process, pressure remains constant while temperature and volume vary. In an adiabatic process, no heat flows in or out of the system while temperature, volume and pressure all vary. We shall derive important results for Q, Δ U and W for each of the processes mentioned above in due course.

The Kelvin-Planck statement of the second law of thermodynamics is:

It is impossible to remove thermal energy from a system at a single temperature and convert it into an equivalent amount of mechanical work without changing the system or the surroundings in some other way.

From an engineering point of view, the most important application of the second law is the limited efficiency of heat engines. A heat engine is a device which continuously converts thermal energy into mechanical work. The thermal efficiency of a heat engine is the ratio of the work done by the engine to the heat absorbed by it from the hot reservoir. Notable examples of heat engine are steam engine and internal combustion engine. There are two types of internal combustion engine: spark ignition engine such as a petrol engine and compression ignition engine such as a diesel engine. The diesel engine has the highest thermal efficiency.

A process which can advance only in forward direction is called an irreversible process. But if a process, operated backwards, takes the system through the same equilibrium states in the reverse order, the original process is known as a reversible process. If a process has to be reversible, it must be quasi-static, non-dissipative and any transfer of heat must take place isothermally. A heat engine cycle which consists only of reversible processes is called a reversible cycle, and the engine is called a reversible engine. In 1824, French physicist Sadi Carnot showed that a reversible engine is the most efficient of all heat engines. Such an engine is known as a Carnot engine, and the cycle followed by it is called Carnot cycle. The formal statement of Carnot theorem is:

No heat engine operating between two given heat reservoirs can be more efficient than a Carnot engine operating between the same two reservoirs.

Carnot efficiency, which is the thermal efficiency of a Carnot engine, is given by the formula:

ηC = 1 - Tc/Th

Here Tc and Th are the temperatures of the cold and hot reservoirs respectively. The result is independent of the working substance used in the engine!

When a heat engine is run in reverse, heat is transferred from the cold reservoir to the hot reservoir and work must be performed on the system. This is the mode of operation of a refrigerator or a heat pump. A Carnot engine run in reverse is called a Carnot refrigerator. Just like Carnot engine, a Carnot refrigerator has the highest coefficient of performance or COP operated between two fixed temperatures.

A common feature of all irreversible processes is that they take the system plus the surroundings towards greater disorder. The concept of entropy, S, was first introduced by Rudolf Clausius. It is an extensive thermodynamic property which gives the measure of a system's disorder. The unit of entropy is joule per kelvin (J/K).

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