Comprehensive WBBSE Class 10 Physical Science Notes Chapter 4 Thermal Phenomena can help students make connections between concepts.

## Thermal Phenomena Class 10 WBBSE Notes

Heat: It is a form of energy which produces sensation of warmth.

Different types of motion:

- Translational motion: Motion along a straight line.
- Vibrational motion: Motion of the molecules about a mean position.
- Rotational motion: Rotation of the molecules about their axes.

Definition of heat with respect to motion: Heat possessed by a body is the total thermal energy of the body and is the sum of kinetic energies of all the individual molecules forming the body due to translational, vibrational and rotational motions of the molecules.

Unit of heat:

- CGS : Calorie
- SI : Joule

One calorie : It is the quantity of heat required to raise the temperature of 1 g water through 1°C

Relation between calorie and Joule : 1 Calorie = 4.18 Joule

Temperature : It is the thermal condition of a body which would determine the direction of flow of heat, when the body is placed in thermal contact with another body.

Measurement of Temperature: Temperatures are measured with a thermometer.

Upper fixed point: It is the temperature of steam from water boiling under a pressure of 76 cm of mercury at sea level and 45° latitude.

Lower fixed point: It is the temperature of melting ice under the same conditions.

Fundamental Internal: The difference between the fixed points of a scale is called fundamental internal.

Different scales of temperature commonly used:

- Celsius scale (by Anders celsius, 1710 , upper fixed point 100°C and Lower fixed point 0°C)
- Fahrenheit scale (by Gabriel Fahrenheit, 1717, upper fixed point = 212° Fand lower fixed point 32°F).
- Absolute or Kelvin scale.

Relation between Celsius and Fahrenheet scale:

\(\frac{C}{5}=\frac{F-32}{9}\)Relation between Celsius and Kelvin scale :

C = K-273.15

Thermal Expansion : Dimensions of all substances generally increases with increase in temperature. This phenomenon is known as thermal expansion.

Types of expansions in solids:

- Linear expansions
- Superficial expansions
- Volume expansions

Coefficient of linear expansion: The coefficient of linear expansion may be defined as the fractional increase in length of a solid per degree rise in temperature.

[α = \(\frac{l_2-l_2}{l_1\left(t_2-t_1\right)}\)]

[l_{1} and l_{2} are the lengths of a bar at temperatures t_{1} and t_{2}° respectively, α = coefficient of linear expansion]

Coefficient of Superficial Expansion: The co-efficient of superficial or surface expansion of a solid is defined as the fractional change in surface area of the solid per degree rise in temperature.

[β = \(\frac{s_2-s_1}{s_1\left(t_2-t_1\right)}\)]

[s_{1}. and s_{2} are the surface areas of a solid at t_{1}° and t_{2}° respectively, β = coefficient of superficial expansion]

Coefficient of cubical expansion: The coefficient of cubical or volume expansion of a solid is defined as the fractional increase in volume of the solid per degree rise in temperature.

[γ = \(\frac{v_2-v_1}{v_1\left(t_2-t_1\right)}\)]

[v_{1}. and v_{2} are the volumes of a solid t_{1}° and t_{2}° respectively, γ = coefficient of superficial expansion]

Coefficient | Unit | Dimension |

α | K^{-1} or °C^{-1} or °F^{-1} |
l^{-1} |

β | K^{-1} or °C^{-1} or °F^{-1} |
l^{-1} |

γ | K^{-1} or °C^{-1} or °F^{-1} |
l^{-1} |

Relation among α, β and γ : \(\left[\alpha=\frac{\beta}{2}=\frac{\gamma}{3}\right]\)

Various applications of solids in our daily life:

- Thermostat Fire Alarm
- Bimetallic Thermometer
- Compensating Rod Type Pendulum
- Harrison’s Grid-iron Pendulum

Apparent expansion of the liquid: If the expansion of the liquid is measured ignoring the expansion of the containing vessel, the expansion is called the apparent expansion of the liquid.

Real expansion of the liquid: When the actual expansion of the liquid is measured by considering the expansion of the containing vessel, it is called real expansion of the liquid.

Real expansion of the liquid = expansion of the vessel + apparent expansion of the liquid

Co-efficient of real expansion of liquids: The coefficient of real or absolute expansion of a liquid is the fraction of its volume

γ_{r} = \(\frac{v_2-v_1}{v_1\left(t_2-t_1\right)}\)

(v_{1} is the initial volume of a given mass of a liquid at t_{1}° and v_{2} is the real volume of the same mass of the liquid at t_{2}°, γ_{r} is the coefficient of real expansion of the liquid).

Co-efficient of apparent expansion of liquids: The coefficient of apparent expansion of the liquid is the traction of its volume by which the liquid appears to expand per degree rise in temperature.

[γ_{r} = \(\frac{v_2-v_1}{v_1\left(t_2-t_1\right)}\)]

(v_{2} is the apparent volume of the liquid at t_{2}°, γ_{a} is the coefficient of apparent expansion of the liquid).

Relation between expansion coefficients of a liquid:

(γ_{r}. is the coefficient of real expansion of the liquid, γ_{a} is the coefficient of apparent expansion of the liquid). γ_{s} is the coefficient of cubic expansion of the material of the vessel)

γ_{r} = \(\frac{v_2^{\prime}-v_1}{v_1\left(t_2-t_1\right)}\)

Variation of density of a liquid with temperature: Let m mass of a liquid has volumes v_{1} and v_{2} at temperatures t_{1}° and t_{2}° respectively. If ρ_{1} and ρ_{2} be the densities of the liquid at t_{1}° and t_{2}° respectively and if γ_{r}, be the coefficient of real expansion of the liquid then,

When a liquid is more expansible than the material of the vessel, there will be, on the whole, an apparent expansion of the liquid. In the reverse case, the liquid will apparently cantact. If two expand equally, the volume of the liquid will appears to remain constant.

A hollow vessel expands as if it were solid having the same volumes, because if the hollow of the vessel were also solid, after expansion it would fit in with outer vessel.

Anomalouis expansion of water: Usually liquids expand on heating. But in the case of water we find deviation from this general behaviour of the liquids within a certain range of temperature. The volume of water is minimum at 4°C and hence its density is maximum at 4°C. This phenomenon is called the anomalous expansion of water.

Conclusion of Hope’s experiment: From Hope’s experiment it is proved that water at bottom which is denset is at 4°C. After sufficiently long time the temperature of the lower thermometer falls slightly due to loss of heat by conduction to the upper regions.

Effect on Marine life: Anomalous expansion of water has great practical importance on the marine life in the cold countries. The temperature of the deeper layers of the water in the pond remains nearly at 4°C and falls gradually at 0°C upwards till the layer of ice is reached. The marine life in the water is thus saved. For the same reason temperature of the bottom of a deep sea remains constant (i.e. 4°C ) throughout the year.

Expansion of a gas at constant Temperature:

Boyle’s Law: The volume of a fixed mass of a gas of constant temperature is inversely proportional to its pressure.

V ∝ \(\frac{1}{P}\) (At constant temperature P is the pressure and V is the volume of a fixed mass of gas)

or V ∝ \(\frac{K}{P}\) (K is the proportionality constant. It depends

or, PV = K = constant

- the mass of the gas
- nature of the gas
- temperature of the gas)

Expansion of a Gas at constant Pressure :

Charles’ Law: The pressure remaining constant, the volume of a given mass of any gas increases (or decreases) by the constant fraction \(\frac{1}{273}\)of its volume of 0°C, for every degree celsius increase (or decrease) of temperature.

V_{t} = V_{0}(1 ± \(\frac{t}{273}\))

v_{0} and v_{t} are the volumes of a given mass of gas at 0°C and t°C respectively, the pressure of the gas remaining constant all through)

Expansion of gas at constant volume:

Pressure Law: Volume remaining constant, the pressure of a given mass of a gas increases (or decreases) by a constant fraction \(\frac{1}{273}\)of its pressure at 0°C for each degree celsius increase (or decrease) of temperature.

P_{t} = P_{0}(1 ± \(\frac{t}{273}\))

(P_{0} and P_{t} are the pressures of a given mass of gas at 0°C and t°C respectively, the volume of the gas remaining constant all through)

Volume Coefficient (γ_{p}) : The volume coefficient of a gas is the fractional increase in the volume of the gas at 0°C for each degree celsius rise in temperature, the pressure remaining constant.

V_{t} = V_{0}(1 + γ_{p} t)

From Charles’ Law, we find γ_{p} = \(\frac{1}{273}\)°C^{-1} = 36.6 × 10_{-4} °C^{-1}

Pressure Coefficient (γ_{ν}): The pressure coefficient of a gas is the fractional increase in pressure of the gas at 0°C for each degree celsius rise in temperature, the volume remaining constant

P_{1} = P_{0}(1 + γ_{v} t)

From Pressure law, we find that γ_{v} = \(\frac{1}{273}\)°C^{-1} = 36.6 × 10_{-4} °C^{-1}

Equality of volume and pressure coefficients : Consider a given mass of a gas at °C having pressure and volume P_{0} and V_{0} respectively. It is heated to a temperature t°C in two alternative ways viz (I) at constant volume, when pressure changes to a P_{t} or (II) at constant pressure, when the volume changes to V_{t}.

In the case I, Pressure Law’s is applicable,

so P_{t} = P_{0}(1 + γ_{v} t)

In case II, Charle’s law is applicable, so V_{t} = V_{0}(1 + γ_{v} t)

In both the cases final temperature is t°C and so according to Boyle’s Law

P_{t} V_{0} = P_{0} V_{t}

or, P_{0} V_{0}(1 + γ_{v} t) = P_{0} V_{0}(1 + γ_{p</sub t)
∴ γv = γr}

Ideal gas and Ideal gas equation: A gas which obeys gas laws is called. A gas which obeys gas laws is called an ideal gas. An ideal gas equation is PV = nRT (R = universal gas constant)

Speciefic heat capacity: Specific heat capacity of a substance is the amount of heat required to rise the temperature of unit mass of the substance through one degree.

Specific heat of water:

- 1 cal g
^{-1}°C^{-1}: CGS system - 4200 Jkg
^{-1}K^{-1}: SI system.

Molar specific heat capacity: Molar specific heat capacity of a substance is the amount of heat required to raise the temperature of one gram mole of the substance through a unit degree.

Molar specific heat at constant volume (C_{v}) : The molar specific heat of a gas at constant volume (C_{v}) is the amount of heat required to raise the temperature of one mole of the gas through one degree keeping the volume constant throughout.

Molar specific heat at constant pressue (C_{p}) : The molar specific heat of a gas at constant pressure (Cp) is the amount of heat required to raise the temperature of one mole of the gas through one degree keeping the pressure constant throughout.

C_{p} is greater than C_{v}

Thermal capacity: Thermal capacity of a substance is the quantity of heat required to raise the temperature of it by 1°.

Water equivalent: Water equivalent of a body is the mass of water which will be heated through 1° by the amount of heat that raises the temperature of the body through 1°.

Fundamental principle of calorimetry

Heat lost by hot body = Heat gained by cold body.

Conditions :

during the process of heat thransfer, there is no heat exchange with the surrounding.

No chemical reaction takes place between the bodies. This is known as fundamental principle of calorimetry.

Latent heat of substance: The amount of heat to be supplied or extracted for changing completely the stake of unit mass of a substance without change of temperature is called the latent heat of the substance for the corresponding change of state.

Melting point and effect of pressure on it :

Melting point: The normal melting point of a solid is the definite temperature at which it melts on heating under normal atmospheric pressure and the temperature remains constant until the melting is complete.

Regelation: The phenomenon of melting of ice under pressure and freezing again on releasing the pressure is called regelation.

Bioling point and e effect of pressure on it:

Bolling point: The normal boiling point of a liquid in the temperature at which a liquid boils under normal atmospheric pressure.

The boiling point of a liquid depends uy on:

- the nature of the liquid
- presence of dissolved substance
- the superincumbent pressure.

Vapour pressure: Whenever a liquid evaporates at any temperature, the vapour exerts a definite pressure on everything in contact. This pressure is called vapour pressure of the liquid at that temperature.

Saturated vapour: If the liquid be allowed to evaporate in a closed space, it is found that after a small time evaporation stops, i.e., t a given temperature, there is a maximum limit to the amount of vapour the space can hold. The space is said to be then saturated with vapour and the vapour is then called saturated vapour.

Difference between Gas and Vapour-Critical Temperature: For every substance in gaseous state there is a certain temperature such that if the substance be below this temperature, it can be liquefied by the application of suitable pressure, and if above this temperature, it cannot be liquified, however large the pressure may be, then the temperature is called the critical temperature for that substance.

Thus a gaseous substance at a temperature above critical temperature is called gas and when it is at a temperature below its critical temperature it is called vapour.

Thermal conduction

Conduction: Conduction is the process of transfer of heat through a substance without any detectable motion of the particles of the substance.

Good conductors: The substances through which heat is conducted easily from one region to the other are called good conductors.

Bad conductors or Insulators: The substances through which heat is not conducted easily from one region to the other are called bad conductors or insulators.

Coefficient of thermal conductivity: The coefficient of thermai conductivity at the material of a substance is numerically equal to the quantity of heat that conducts in one second normally through a slab of unit length and unit area, the difference of temperature between its end faces being one degree.

Unit of thermal conductivity

CGS: Cal cm^{-1} S^{-1}0 C^{-1}

SI: Jm^{-1} S^{-1} K^{-1} or Wm^{-1} k^{-1}

Dimension: [MLT^{-3} θ^{-1}]

Thermometric conductivity: The rate of rise of temperature during the variable state is proportional to K / P_{3} (where K = thermal conductivity of the material, P_{s} = specific heat). This ratio is known as thermometric conductivity or the thermal conductivity per thermal capacity per unit volume.

Unit of thermometric conductivity:

CGS: cm^{2} s^{-1} ; SI: m^{2} s^{-1}

Dimension of thermometric conductivity: [M^{0} L^{2} T^{-1}]

Although thermal conductivity of iron is more than that of lead, diffusivity of lead is more and they under similar conditions of heat flow, the temperature of different sections of the lead bar would rise more rapidly than iron bar.

Applications of conductivity:

ICE is packed in saw dust, because air which is bad conductors of heat being trapped in the saw dust prevents transfer of heat from the surrounding to the ice. So ice does not melt.

Cooking utensils are provided with wooden or plastic handles, as wood or plastic are bad conductors of heat, so we can hold the hot utensils with the help of these handles.

Wearing two cotton shirts of half the thickness each is better than a single shirt of double the thickness in winter. There is a layer of bad conductor air entrapped between the two shirts providing additional protection from heat conduction from the body.

In winter, birds often swell their feathers, thereby enclosing air between their bodies and feathers and thus does not allow flow of heat from the bodies of the birds and keeps them warm.

Convection of Heat: Convection is the process by which heat is transmitted through a liquid or gas from a hotter point to a colder point due to the bodily motion of the heated particles of the substances.

It may be noted that although mercury is a liquid, it is heated by conduction and not by canvection.

Radiation: Radiation is the transmission of heat from a hot body to a cold body without the help of any medium and without appreciable heating of the intervening medium if any.

Some basic characteristics of thermal radiations are:

- (i) They travel along straight line with velocity of light.
- They require no medium for their propagation and even if there be intervening medium, the medium is not affected.
- They obey inverse square law i.e. their intensity varies inversely as the square of the distance from the source.
- They can be reflected and refracted like light.
- They also exhibit the phenomena of interference, diffraction and polarisation.

The reflecting power of a body (Reflectance) : It is the ratio of the amount of thermal radiations reflected by the body in a given time to the total amount of thermal radiation incident on the body in the same time.

The absorbing power of a body (absorbtance): It is the ratio of the amount of thermal radiations absorbed by the body in a given time to the total amount of thermal radiations incident on the body in the same time.

The transmitting power of a body (transmittance): It is the ratio of the amount of thermal radiations transmitted through the body in a given time to the total amount of thermal radiations incident on the body in the same time.

Perfectly Black body; A perfectly black body is that which absorbs completely the radiations of all the wavelengths on it.

Kirchoff’s Law : It states that the ratio of emissive power to absortive power corresponding to a particular wavelength and at any given temperature is always a constant for all bodies, the constant being equal to the emissive power of a perfectly black body at the same temperature and corresponding to the same wavelength.

Stefan’s Law: It state that the amount of heat energy emitted per second by unit area of a perfectly black body is directly proportional to the fourth power of absolute temperature of the body.

Wen’s displacement Law: It states that the wavelength of maximum intensity of emission of black body radiation is inversely proportional to the absolute temperature of the body.

Newton’s Law of cooling: It states that the rate of loss of heat of a liquid is directly proportional to the difference in temperatures at the liquid and the surroundings, provided the difference in temperature is small.

Green house effect: Green house effect is an example of selective absorption of heat by glass. The amount of heat transmitted through a substance depends on temperature of the source of heat.

Global warming: CO_{2}, water vapour, methane, nitrous oxide, tropospheric ozone, chlorofluoro carbon compounds, halogen compounds etc. on increasing the amount of green house gases in the atmosphere, the temperature of earth.

Effect of global warming:

- Possibility of increasing the sea level
- Effect on atmosphere
- Effect on forest and agriculture