Heat Transfer: Class 11 Physics Notes, Definition, Tyes, & Formulas

Updated on May 19, 2025 10:32 IST

Heat Transfer is the study of energy movement or transfer from one system to another without losing the energy in the surrounding system. Energy can transfer in three ways: conduction, convection, and radiation. Understanding the fundamentals of heat transfer mechanisms can help explain natural phenomena and improve the design of thermal systems such as heaters, insulators, radiators, etc.

Heat Transfer is an important topic in Class 11 Physics Chapter 10 Thermal Properties of Matter. Through this article, we have discussed the heat transfer definition and its types. Students can go through the article and understand the Class 11 Physics heat transfer topics in detail. Also, Class 11 Physics Chapter 10 NCERT solution for exercise problems is available online. Practice the NCERT Class 11 Physics Solutions to score good marks in the CBSE board exam. NCERT Solutions are considered the best study material to prepare for the exam. They consist of a number of questions based on the previous year CBSE board exam.

Table of content

What is Heat Transfer?
Types of Heat Transfer
Conduction
Steady State
Thermal Resistance to Conduction
Slabs in Parallel and Series
Slabs in Parallel
Convection
Radiation
Prevost Theory of Exchange
Perfectly Black Body and Black Body Radiation
Absorption, Reflection and Emission of Radiation
Kirchoff's Law
Nature of Thermal Radiations : (Wien's Displacement Law)
Stefan-Boltzmann’s Law

What is Heat Transfer?

We can explain heat transfer as the movement of thermal energy from one system to another or one part of the system to another due to a temperature difference. Every material has a different thermal conductivity.

Importance of Heat Transfer

Knowledge of heat transfer is important to maintain the balance in nature, designing machines and structures.

Daily Life Application
- Ironing clothes, boiling water and cooking food all involve heat transfer.
- Controlling the heat transfer using insulation or ventilation can keep cool in summer and warm in winter.
Engineering and Technology
- The proper functioning of engines, refrigerators and air conditioning depends on the heat transfer properties of the devices.
- We can control the overheating and damage of electronic devices through thermal management.
Environmental Significance
- The heat transfer between earth, atmosphere, and oceans influences the weather patterns, oceans currents, and climate change.
Medical and Biological Systems
- Regulation of human body temperature depends on the heat transfer through conduction, convection, and radiation.
- Incubators and heating pads use controlled heat transfer for patient care.
Industrial Application
- Controlling heat transfer in power plants, chemical factories, and manufacturing industries can improve efficiency and safety.

Types of Heat Transfer

Heat is a form of energy that moves from a warmer object to a cooler one due to a temperature difference. This energy transfer can happen in three main ways:

Conduction

Convection

Radiation

Conduction

Conduction is the process where heat travels through a material without the material itself moving. Imagine holding one end of a metal rod while the other end is in a flame. Eventually, your hand feels the heat, not because the metal moved, but because the energy passed from atom to atom.

In solids, especially metals, atoms vibrate more intensely when heated. These vibrations are passed along to neighbouring atoms, transferring heat through the material. Let’s consider a flat slab with area A and thickness L, where one side is at a higher temperature (Tₕ) and the other at a lower temperature (T꜀). The heat flow Q through the slab over time t is

Consider a slab of face area A, Lateral thickness L, whose faces have temperatures $T_{H} a n d T_{C} (T_{H} > T_{C})$ . Now, consider two cross sections in the slab at positions A and B separated by a lateral distance of dx. Let the temperature of face A be T and that of face B be $T + Δ T$ . The experiments show that Q, the amount of heat crossing the area A of the slab at position x in time t, is given by

Here, K is a constant depending on the material of the slab and is named the thermal conductivity of the material, and the quantity $(\frac{d T}{d x})$ is called the temperature gradient. The (–) sign in equation (2.1) shows that heat flows from high to low temperature $(Δ T$ is a -ve quantity.

Steady State

If the temperature of a cross-section at any position x in the above slab remains constant with time (remember, it does vary with position x), the slab is said to be in steady state.

Remember steady-state is distinct from thermal equilibrium for which temperature at any position (x) in the slab must be same.

For a conductor in steady state there is no absorption or emission of heat at any cross-section. (As temperature at each point remains constant with time). The left and right face are maintained at constant temperatures $T_{H} a n d T_{C}$ respectively, and all other faces must be covered with adiabatic walls so that no heat escapes through them and same amount of heat flows through each cross-section in a given Interval of time.

Hence, $Q_{1} = Q = Q_{2}$ . Consequently, the temperature gradient is constant throughout the slab.

Hence, $\frac{d T}{d x} = \frac{Δ T}{L} = \frac{T_{f} - T_{i}}{L} = \frac{T_{C} - T_{H}}{L}$

= and $\frac{Q}{t} = K A \frac{Δ T}{L}$ .... (3.1)

Here, Q is the amount of heat flowing through a cross-section of the slab at any position in a time interval of t.

Thermal Resistance to Conduction

If you are interested in insulating your house from cold weather or for that matter, keeping the meal hot in your tiffin-box, you are more interested in poor heat conductors, rather than good conductors. For this reason, the concept of thermal resistance R has been introduced.

For a slab of cross-section A, Lateral thickness L and thermal conductivity K,

$R = \frac{L}{K A}$ ... (4.1)

In terms of R, the amount of heat flowing through a slab in steady-state (in time t)

$\frac{Q}{t} = \frac{(T_{H} - T_{C})}{R}$

If we name $\frac{Q}{t}$ as thermal current i_T

then, $i_{T} = \frac{T_{H} - T_{C}}{R}$ (4.2)

This is mathematically equivalent to OHM’s law, with temperature playing the role of electric potential. Hence, results derived from OHM’s law are also valid for thermal conduction.

Moreover, for a slab in steady state, we have seen earlier that the thermal current $i_{L}$ remains the same at each cross-section. This is analogous to Kirchhoff’s current law in electricity, which can now be very conveniently applied to thermal conduction.

Slabs in Parallel and Series

Slabs in series (in steady state)

Consider a composite slab consisting of two materials having different thicknesses $L_{1} a n d L_{2} d i f f e r e n t c r o s s$ $s e c t i o n a l a r e a s A_{1} a n d A_{2}$ and different thermal conductivities. $K_{1} a n d K_{2} .$ The temperature at the outer surface of the slab is maintained at $T_{H} a n d T_{C}$ , and all lateral surfaces are covered by an adiabatic coating.

Let the temperature at the junction be T, since steady state has been achieved thermal current through each slab will be equal. Then the thermal current through the first slab.

$i = \frac{Q}{t} = \frac{T_{H} - T}{R_{1}} o r T_{H} - T = i R_{1}$ ... (5.1)

and that through the second slab,’

$i = \frac{Q}{t} = \frac{T - T_{C}}{R_{2}} o r T - T_{C} = i R_{2}$ ... (5.2)

adding eqn. 5.1 and eqn 5.2

$T_{H} - T_{L} = (R_{1} + R_{2}) i o r i = \frac{T_{H} - T_{C}}{R_{1} + R_{2}}$

Thus, these two slabs are equivalent to a single slab of thermal resistance $R_{1} + R_{2}$ .

If more than two slabs are joined in series and are allowed to attain steady state, then the equivalent thermal resistance is given by

$R = R_{1} + R_{2} + R_{3} + \dots$ ...(5.3)

Slabs in Parallel

Consider two slabs held between the same heat reservoirs, with their thermal conductivities $K_{1} a n d K_{2} a n d c r o s s$ $s e c t i o n a l a r e a s A_{1} a n d A_{2}$

then $R_{1} = \frac{L}{K_{1} A_{1}}, R_{2} = \frac{L}{K_{2} A_{2}}$

thermal current through slab 1

$i_{1} = \frac{T_{H} - T_{C}}{R_{1}}$

and that through slab 2

$i_{2} = \frac{T_{H} - T_{C}}{R_{2}}$

Net heat current from the hot to cold reservoir

$i = i_{1} + i_{2} = (T_{H} - T_{C}) (\frac{1}{R_{1}} + \frac{1}{R_{2}})$

Comparing with $i = \frac{T_{H} - T_{C}}{R_{e q}}$ , we get,

$\frac{1}{R_{e q}} = \frac{1}{R_{1}} + \frac{1}{R_{2}}$

If more than two rods are joined in parallel, the equivalent thermal resistance is given by

$\frac{1}{R_{e q}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} + \dots$ .... (5.4)

Can you now see how the following facts can be explained by thermal conduction?

(a) In winter, iron chairs appear to be colder than the wooden chairs.

(b) Ice is covered in gunny bags to prevent melting.

(c) Woollen clothes are warmer.

(d) We feel warmer in a fur coat.

(e) Two thin blankets are warmer than a single blanket of double the thickness.

(f) Birds often swell their feathers in winter.

(g) A new quilt is warmer than old one.

(h) Kettles are provided with wooden handles.

(i) Eskimo's make double-walled ice houses.

(j) Thermos flask is made double-walled.

Convection

When heat is transferred from one point to the other through the actual movement of heated particles, the process of heat transfer is called convection. In liquids and gases, some heat may be transported through conduction.

But most of the transfer of heat in them occurs through the process of convection. It occurs through the aid of Earth’s gravity. Normally, the portion of fluid at a greater temperature is less dense, while that at a lower temperature is denser. Hence, hot fluid rises while colder fluid sinks, accounting for convection. In the absence of gravity, convection would not be possible.

Also, the anomalous behaviour of water (its density increases with temperature in the range 0-4ºC) give rise to interesting consequences vis-a-vis the process of convection. One of these interesting consequences is the presence of aquatic life in temperate and polar waters. The other is the rain cycle.

Can you now see how the following facts can be explained by thermal convection?

(a) Oceans freeze from top to down and not from bottom to up. (This fact is singularly responsible for the presence of aquatic life in temperate and polar waters.)

(b) The temperature at the bottom of deep oceans is invariably 4ºC, whether it is winter or summer.

(c) You cannot illuminate the interior of a lift in free fall or an artificial satellite of Earth with a candle.

(d) You can illuminate your room with a candle.

Radiation

The process of the transfer of heat from one place to another place without heating the intervening medium is called radiation. The term radiation used here is another word for electromagnetic waves. These waves are formed due to the superposition of electric and magnetic fields perpendicular to each other and carry energy.

Properties of Radiation:

(a) All objects emit radiation simply because their temperature is above absolute zero, and all objects absorb some of the radiation that falls on them from other objects.

(b) Maxwell, based on his electromagnetic theory, proved that all radiations are electromagnetic waves and their sources are vibrations of charged particles in atoms and molecules.

(c) More radiations are emitted at higher temperatures of a body and less at lower temperatures.

(d) The wavelength corresponding to maximum emission of radiation shifts from longer wavelengths to shorter wavelengths as the temperature increases. Due to this, the colour of a body appears to be changing. Radiations from a body at NTP have predominantly infrared waves.

(e) Thermal radiation travels with the speed of light and moves in a straight line.

(f) Radiation is electromagnetic waves and can also travel through a vacuum.

(g) Similar to light, thermal radiations can be reflected, refracted, diffracted and polarized.

(h) Radiation from a point source obeys the inverse square law (intensity ).

Prevost Theory of Exchange

According to this theory, all bodies radiate thermal radiation at all temperatures. The amount of thermal radiation emitted per unit time depends on the nature of the emitting surface, its area and its temperature.

The rate is faster at higher temperatures. Besides, a body also absorbs part of the thermal radiation emitted by the surrounding bodies when this radiation falls on it. If a body radiates more than what it absorbs, its temperature falls. If a body radiates less than what it absorbs, its temperature rises. And if the temperature of a body is equal to the temperature of its surroundings, it radiates at the same rate as it absorbs.

Perfectly Black Body and Black Body Radiation

A perfect black body absorbs all radiation that hits it. While no real object is perfect, materials like lamp-black come close.

Fery’s black body is a practical model: a cavity with a small opening painted black inside. Radiation entering the hole gets absorbed after multiple reflections.

Absorption, Reflection and Emission of Radiation

The total incident radiation on a body is either:

Reflected (r)

Transmitted (t)

Absorbed (a)

So, $Q = Q_{r} + Q_{t} + Q_{a}$

$1 = \frac{Q_{r}}{Q} + \frac{Q_{t}}{Q} + \frac{Q_{a}}{Q}$ ; 1 = r + t + a

where r = reflecting power, a = absorptive power

and t = transmission power.

(i) r = 0, t = 0, a = 1, perfect black body

(ii) r = 1, t = 0, a = 0, perfect reflector

(iii) r = 0, t = 1, a = 0, perfect transmitter

Absorptive power :

In particular absorptive power of a body can be defined as the fraction of incident radiation that is absorbed by the body.

$a = \frac{E n e r g y a b s o r b e d}{E n e r g y i n c i d e n t}$

As all the radiations incident on a black body are absorbed, a=1 for a black body.

Emissive power:

Energy radiated per unit time per unit area along the normal to the area is known as emissive power.

$E = \frac{Q}{Δ A Δ t}$ (Notice that, unlike absorptive power, emissive power is not a dimensionless quantity).

Spectral Emissive power

Emission at a specific wavelength λ is known as spectral emissive power.

If E is the total emissive power and is the spectral emissive power, they are related as follows,

$E = \int_{0}^{\infty} E_{λ} d λ a n d \frac{d E}{d λ} = E_{λ}$

Emissivity:

$e = \frac{E m i s s i v e p o w e r o f a b o d y a t t e m p e r a t u r e T}{E m i s s i v e p o w e r o f a b l a c k b o d y a t s a m e t e m p e r a t u r e T} = \frac{E}{E_{0}}$

Ratio of a body’s emissive power to that of a black body at the same temperature.

Kirchoff's Law

The ratio of emissive to absorptive power is the same for all materials at the same temperature and wavelength. This means good emitters are also good absorbers.

$\frac{E (b o d y)}{a (b o d y)} = E (b l a c k b o d y)$

Hence, we can conclude that good emitters are also good absorbers.

Nature of Thermal Radiations : (Wien's Displacement Law)

From the energy distribution curve of black body radiation, the following conclusions can be drawn :

(a) The higher the temperature of a body, the higher is the area under the curve i.e. more amount of energy is emitted by the body at higher temperature.

(b) The energy emitted by the body at different temperatures is not uniform. For both long and short wavelengths, the energy emitted is very small

(c) For a given temperature, there is a particular wavelength for which the energy emmitted is is maximum.

(d) With an increase in the temperature of the black body, the maxima of the curves shift towards shorter wavelengths.

Wien's displacement law states that as temperature increases, the peak wavelength of emitted radiation from a black body shifts to shorter wavelengths . This can be expressed as:

i.e.

Here, $b = 0.282 c m - K$ -k, is the Wien’s constant.

Where λₘ is the wavelength of maximum intensity and T is the temperature. The peak emission's wavelength is inversely proportional to temperature.

Stefan-Boltzmann’s Law

The total energy radiated by a black body is proportional to the fourth power of its temperature:

$u = σ A T^{4}$ ..... (13.1)

Where $σ i s S t e f a n' s c o n s t a n t = 5.67 \times 10^{- 8} W / m^{2} K^{4}$

A body which is not a black body absorbs and hence emits less radiation than

For such a body, $u = σ A T^{4}$ .....(13.2)

where e = emissivity (which is equal to absorptive power), which lies between 0 to 1

With the surroundings of temperature, the net energy radiated by an area A per unit time.

Physics Thermal Properties of Matter Exam

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Heat Transfer: Class 11 Physics Notes, Definition, Tyes, & Formulas

What is Heat Transfer?

Types of Heat Transfer

Conduction

Steady State

Thermal Resistance to Conduction

Slabs in Parallel and Series

Slabs in Parallel

Convection

Radiation

Prevost Theory of Exchange

Perfectly Black Body and Black Body Radiation

Absorption, Reflection and Emission of Radiation

Kirchoff's Law

Nature of Thermal Radiations : (Wien's Displacement Law)

Stefan-Boltzmann’s Law

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Other Class 11th Physics Chapters

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