UNIT 11- THERMAL PROPERTIES OF MATTER

11.2 Heat We may define heat as a form of energy. This energy can lead to an increase or decrease in the internal energy of an object or body where the body remains static and no external work is done either on or by the body. The S.I unit of heat is Joule (J) OR cgs or practical unit is calorie 1 calorie is defined as the amount of heat required to raise the temperature of 1 gram of a substance through 1 degree Celsius.

11.2 Temperature We have already understood that heat is the form of energy that leads to an increase or decrease in the internal energy of the body. This internal energy is also known as temperature. In other words, the temperature is a measurement by which we may measure the degree of hotness or coolness present in a body.

Temperature is measured in degrees. The measuring unit for temperature in Celsius and Fahrenheit. However, these measures are used in your daily life. For scientific measurement, we use the Kelvin scale.

Let us now find out the equation for the three measurements.

°F = (9/5 × °C) +32

°C = (9/5)(°F- 32)

K = C + 273°

11.3Measurement of temperature A thermometer is a device which uses the property of matter that changes sufficiently with temperature. These properties include pressure, volume, resistance of metal & thermos emf. A thermometer calibrated for a particular scale uses two reference points, the ice point and steam point at standard pressure.

11.5 Thermal Expansion

If the temperature increases, then the volume of the material also increases. Generally, this is known as

thermal expansion. We can express it in this way that it is the fractional change in length or volume per

unit change in temperature.

In case of expansion of a solid, normally linear expansion coefficient is usually employed. The thermal

expansion of solid, is described in terms of change in length, height, and thickness. For liquid and gas,

the volume expansion coefficient is more useful. Generally, if the material is a fluid then we can describe

it in terms of change in volume.

Among the atoms and molecules, the bonding forces vary from material to material. Characteristics of

elements and compounds are known as expansion coefficient.

If a crystalline solid has the same structural configuration throughout, (isometric) then in all dimensions

of crystal the expansion will be uniform.

If the crystal is not isometric then expansion coefficient is also different for different crystallographic

directions and as the temperature will change then the crystal will also change the shape. Softer

materials have a higher coefficient of expansion (CTE) but harder materials like tungsten have lower CTE.

Types of Expansion

Linear Expansion: Linear expansion is defined as the increase in the length of the solid.

Example: If we will consider one rod where the length of the rod is l, and we will increase the

temperature of a rod by a small amount. So Linear Expansion is given by:

The Coefficient of linear expansion of the given solid is denoted as α. Its unit is per degree Celsius in the

CGS and in the SI system it is per kelvin.

Area or superficial Expansion: Superficial expansion is defined as the increase in surface area of the

solid on heating. If you consider at 0 0C area of a solid is A0 then its area at t 0c is given by: A0 (l+βt). Unit

of β is 0C-1 or K-1. Where β is known as the coefficient of superficial expansion

Volume Expansion: Volume expansion is defined as the increase in the volume of the solid on heating.

With a change in temperature ∆t the change in volume of a solid is given by ∆v=γ*V*∆t where the

coefficient of volume expansion is y.

6α = 3β = 2γ (refer class note)

These three coefficients of expansion for a given solid are not constant because these values totally

depend on the temperature. Examples of thermal expansion in our daily life are thermometers, riveting,

on wooden wheels fixing metal tires etc.

Note:

Heating a liquid in a container causes both expansion of liquid as well as container. Such an

expansion is called apparent expansion. Otherwise its real expansion.

So γ (apparent expansion) = γ (real expansion) +γ (container expansion)

When a solid or liquid undergoes volume expansion it also undergoes a change in its density.

Δρ/ρ’ΔT = γ

Gases show expansion at ordinary temperature more than solids and liquids. Therefore γ is

relatively independent for solids and liquids but it is dependent on temperature for gases.

11.6 Specific heat capacity

Specific heat of a solid or liquid is the amount of heat that raises the temperature of a unit mass of the solid through 1° C. We symbolize it as C/S. In S.I unit, it is the amount of heat that raises the temperature of 1 kg of solid or liquid through 1K. Its unit in S.I system is always given as J kg-1 K-1 and CGS as cal g-1 C-1. If the amount of heat, ∆Q, required to raise the temperature of mass m through ∆T, then the formula for specific heat is given by:

C= ∆Q/m*∆T or ∆Q=m C ∆T. Molar Specific Heat The Molar specific heat of a solid or liquid of a material is the heat that you provide to raise the temperature of one mole of solid or liquid through 1K or 1° C. We represent it as C. Its unit is J mol-1K-1. So, to raise the temperature of µ/n moles of solid through ∆T, you would need an amount of heat equal to ∆Q=µ C ∆T. The molar specific heat capacity of a substance is nothing but the amount of heat you need to provide to raise the temperature of one gram molecule of the substance through one degree centigrade. It is denoted by C. Specific heat of water is taken to be 1. This is because of the reason that we defined unit of heat (calorie) by making use of water.

Specific Heat at Constant Pressure or Volume The volume of solid remains constant when heated through a small range of temperature. This is

known as specific heat at a constant volume. It is denoted as CV. The pressure of solid remains constant when heated through a small range of temperature. This is

known as specific heat at constant pressure which can be denoted as CP. The behavior of gas when heat is supplied, the pressure and volume change in temperature and the amount of heat required to raise the temperature for 1gm of gas through 1°C depends on the way gas is heated. You can use several sets of values of P and V to heat the gas. Therefore, specific heat possesses infinite values. The specific heat of the gas is not constant if you do not supply a constant amount of heat. So, you must have specific heat at a constant volume or pressure. For an ideal gas,

CP – CV = nR where CP is heat capacity at constant pressure, CV is heat capacity at constant volume, n is amount of substance, and R=8.3144598(48) J mol−1 K and is the molar gas constant. Applications The utensils used for cooking use a material of low specific heat. You can heat their bottoms quickly.

This is because they have aluminium or copper polished bottoms. The handle of these utensils is made of high specific heat material to sustain the heat and to save our hands.

Insulators use materials of high specific heat. For example wood. House made of wood are more useful in High temperature or Low-temperature area.

Due to a high specific heat of water, in swimming pool, water used to be cool as compared to the temperature outside.

Latent Heat When the change of state is studied carefully, we see that the temperature of a substance remains constant during a change in the state! This is very strange. As if the change in state opens up new portals or spaces where our supplied energy hides. Therefore we call this hidden energy, the latent or the hidden heat. Let us understand this with an example: Suppose we have a block of ice we want to convert to water. We all know that ice turns to water and vice versa at 0°C. Now assume we start heating ice at 0°C. You will observe that when we do so, the temperature of ice does not change. It starts converting to water but the temperature does not rise until the entire ice block has been converted to water. If a mass ‘m’ of any substance undergoes a change in state by absorbing an amount of heat, Q at a constant Temperature T, then we have:

L = Q/m or Q = mL All the heat supplied to the ice at 0 0C is used by the ice to change its phase from solid to liquid. Thus the heat supplied is not used up to raise the temperature of the substance. There are 2 kinds of Latent heat: Latent Heat of Fusion The heat energy supplied per unit mass of a substance at its melting point to convert the state of the substance from solid to liquid is known as Latent heat of Fusion. Latent heat of Fusion of water is 334 Joules/gram of water.

Latent Heat of Vaporization The heat that a substance absorbs per unit mass at its boiling point to convert the phase of the substance from liquid to gas is the Latent heat of Vaporization. Latent heat of Vaporization of water is 2230 Joules/gram of water. Now similarly, if you want to convert the phase of a substance from a gas to liquid or from liquid to solid you need to cool the substance to its boiling point or melting point as the conditions demand and then extract the amount of Latent heat to facilitate the phase change. 11.7Calorimetry

(formula refer note)

11.9 Heat Transfer

11.9.1Conduction:

Thermal conduction is the process in which thermal energy is transferred from the hotter part of a body to the colder one or from hot body to a cold body in contact with it without any transference of material particles

Coefficient of Thermal Conductivity: It is defined as amount of heat conducted during steady state in unit time through unit area of any cross-section of the substance under unit temperature gradient, the heat flow being normal to the area.

Units SI J/mSk or W/mK Larger the thermal conductivity, the greater will be rate of heat energy flow for a given temperature difference. • K metals > K non metals • Thermal conductivity of insulators is very low. Therefore, air does not let the heat energy to be conducted very easily. • For combinations of rods between two ends kept at different temperatures, we can use the concept of equivalent thermal conductivity of the composite rod. The term

TC TD/L in the above equation is called as Temperature Gradient.

Temperature Gradient: The fall in temperature per unit length in the direction of flow of heat energy is called as Temperature Gradient

Units SI K/m • The term Q, (i.e.) rate of flow of heat energy can also be named as heat current • The term (L/KA) is called as thermal resistance of any conducting rod. Thermal Resistance: Obstruction offered to the flow of heat current by the medium

Units K/W

11.9.2 Convection The process in which heat is transferred from one point to another by the actual movement of the heated material particles from a place at higher temperature to another place of lower temperature is called as thermal convection. • If the medium is forced to move with the help of a fan or a pump, it is called as forced convection. If the material moves because of the differences in density of the medium, the process is called natural or free convection.

11.9.3Radiation It is a process of transmission of heat in which heat travels directly from one place to another without the agency of any intervening medium. • This radiation of heat energy occurs in the form of EM waves. • These radiators are emitted by virtue of its temperature, like the radiation by a red hot iron or light from a filament lamp. • Everybody radiates energy as well as absorbs energy from surroundings. • The proportion of energy absorbed depends upon the colour of the body

UNIT -12THERMODYNAMICS

It is the study of interrelations between heat and other forms of energy

12.1Thermodynamic System: A collection of large number of molecules of matter (solid, liquid or gas) which are so arranged that these possess certain values of pressure, volume and temperature forms a thermodynamic system. • The parameters pressure, volume, temperature, internal energy etc which determine the state or condition of system are called thermodynamic state variables. In thermodynamics we deal with the thermodynamic systems as a whole and study the interaction of heat & energy during the change of one thermodynamic state to another

12.3 Zeroth law of thermodynamics: According to zeroth law, when the thermodynamics systems A and B are separately in thermal equilibrium with a third thermodynamic system C, then the systems A and B are in thermal equilibrium with each other also.

12.5 First Law of Thermodynamics:

Let ΔQ = Heat supplied to the system by the surroundings ΔW = Work done by the system on the surroundings ΔU = Change in internal energy of the system.

First law of thermodynamics states that energy can neither be created nor be destroyed. It can be only transformed from the form to another. Mathematically: ΔQ=ΔU+ΔW Sign Conventions:

• When heat is supplied to the system, then Q is positive and when heat is withdrawn from the system, ΔQ is negative. • When a gas expands, work done by the gas is positive & when a gas contracts then w is negative • ΔU is positive, when temperature rises and U is negative, when temperature falls. 12.8 Application of the First of Law of Thermodynamics

1. Isothermal Process

Description: A thermodynamic process in which temperature remains constant Condition: The walls of the container must be perfectly conducting to allow free exchange of heat between gas and its surroundings. The process of compression or expansion should be slow so as the provide time for exchange of heat. These both conditions are perfectly ideal. Equation of State: T = Constant (Derivation refer note) Indicator diagram:

2. Adiabatic Process

Description: When there is not heat exchange with surroundings Conditions: The walls of the container must be perfectly non-conducting in order to prevent any exchange of heat between the gas and its surroundings. The process of compression or expansion should be rapid so there is no time for the exchange of heat. These conditions are again ideal condition and are hard to obtain Equation of State:

Pvr = constant Or TVr –1 = constant Indicator Diagram:

12.9 Heat Engines

It is a device that converts heat energy into mechanical energy.

Key Elements:

• A source of heat at higher temperature • A working substance • A sink of heat at lower temperature. Working:

• The working substance goes through a cycle consisting of several processes. • In some processes it absorbs a total amount of heat Q1 from the source at temperature T1. • In some processes it rejects a total amount of heat Q2 to the sink at some lower temperature T2. • The work done by the system is a cycle is transferred to the environment via some arrangement.

12.10Refrigerator and Heat Pumps

A refrigerator or heat pump is a device used for cooling things. Key Elements:

• A cold reservoir at temperature T2. • A working substance. • A hot reservoir at temperature T1 Working

• The working substance goes through a cycle consisting of several process. • A sudden expansion of the gas from high to low pressure which cool it and converts it into a vapour-liquid mixture. • Absorption by the cold fluid of heat from the region to be cooled converting it into vapour. • Heating up of the vapour due to external work done on the working substance. • Release of heat by the vapour to the surroundings bringing it to the initial state and completing the cycle.

12.11

UNIT 13KINETIC THEORY OF GASES 13.4 Assumptions of Kinetic Theory of Gases

1. Every gas consists of extremely small particles known as molecules. The molecules of a given gas are

all identical but are different from those of another gas.

2. The molecules of a gas are identical spherical, rigid and perfectly elastic point masses.

3. Their molecular size is negligible in comparison to intermolecular distance (10-9 m).

4. The speed of gas molecules lies between zero and infinity (very high speed).

5. The distance covered by the molecules between two successive collisions is known as free path and

mean of all free path is known as mean free path.

6. The number of collision per unit volume in a gas remains constant.

7. No attractive or repulsive force acts between gas molecules.

8. Gravitational to extremely attraction among the molecules is ineffective due small masses and very

high speed of molecules.

13.4.1& 13.4.2 PRESSURE EXERTED BY A GAS IN TERMS OF KINETIC THEORY &

KINETIC INTERPRETATION OF TEMPERATURE: (DERIVATION REFER NOTE BOOK)

13.6 DEGREES OF FREEDOM: (DERIVATION REFER NOTE)

13.5

13.7 Mean free path