Thermal Physics - Physics JEE Advanced

JEE Advanced Physics Chapters

1

General Physics

5

Electromagnetic Waves 

2

Mechanics

6

Optics

3

Thermal Physics

7

Modern Physics

4

Electricity and Magnestism

Name of the Concept

Key Points

Heat Transfer

• This process of heat transfer takes place in three forms

• Conduction( this involves physical contact between two objects such that the heat transfer takes place from warmer body to cooler body)

• Convection( this takes place in the form of convection currents and it doesn’t require any physical touch between two bodies.)

• Radiation( this takes place in the form of rays that lie in the electromagnetic spectrum.)

Newton’s Law of Cooling

• This law states that the heat loss from anybody is directly proportional to the difference in temperature in the body and the corresponding surroundings.

• The formula for the law is given by

$\dfrac{dT}{dt} = -k(T-T_{s})$

Zeroth Law of Thermodynamics

• The law states that two systems in thermal equilibrium with a third system separately are in thermal equilibrium with each other.

First Law of Thermodynamics 

• This law states that the energy supplied to the system goes in part to increase the internal energy of the system and rest in work done on the surroundings.

• The above statement can be formulated as-

$\triangle Q $ = $\triangle U$ + $\triangle W$

• This law is in accordance with the Law of Conservation of Energy.

Heat Capacity 

• Heat Capacity denoted by “ S” is defined as the minimum amount of heat required to raise the temperature of a substance from T to T + $ \triangle T$

• This is a mass-dependent property.

S = $\dfrac{\triangle Q}{\triangle T}$

Specific Heat Capacity

• Specific heat capacity denoted by “s” is defined as

s = $\dfrac{S}{m}$ or $\dfrac{\triangle Q}{m \triangle T}$

• This clearly shows that specific heat capacity is independent of mass and is a characteristic value of substance only.

Thermodynamic  State Variables

• These variables are of two types:-

• Extensive - These are those variables that are dependent on the mass of the system or the amount of quantity present in that system. E.g. Internal Energy, Volume and Mass.

• Intensive- These quantities are independent of the mass of the system like temperature, Pressure, Density.

Cyclic Process

• This process is defined as if a system returns to its initial state after performing a continuous cycle such that the change in internal energy is zero.

Heat Engine

• Heat engine is a device through which the cyclic process takes place in a system.

• It consists of a working substance which itself is a system.

• If a heat engine has a source i.e. a hot reservoir having heat $Q_{1}$  at temp $T_{1}$ and a sink i.e. cold reservoir which releases heat $Q_{2}$ at temp $T_{2}$  then its efficiency is defined as

• $\eta = \dfrac{W}{Q_{1}}$

Where W is the work done by the system in a cyclic process.

Second Law of Thermodynamics

• The law states that heat can’t be transferred from a body at a lower temperature to a body at a higher temperature without any addition of energy. 

Reversible and Irreversible processes

• A thermodynamic process can be said to be reversible if the process returns to its original position from the initial i.e. both system and surroundings return to their original states without any change in the universe.

Irreversible Processes are those that cannot return to their original conditions with the same path if reversed.

Carnot Engine

• The Carnot engine is the only possible reversible that works between two reservoirs at different temperatures. 

• Efficiency of Carnot engine is given as

$\eta = 1-\dfrac{T_{2}}{T_{1}}$

• Another major formula used in Carnot Cycle which shows the interdependence of system is

$\dfrac{T_{1}}{T_{2}}$ = $\dfrac{Q_{1}}{Q_{2}}$

Processes in Carnot Cycle

• Process 1-2 is Isothermal Expansion taking place at a constant temperature.

• Process 2-3 is Adiabatic Expansion such that no heat is absorbed or lost by the system.

• Process 3-4 is Isothermal Compression where heat is rejected by the system.

• Process 4-1 is Adiabatic Compression.

Distribution of Molecular Speeds

• For a given mass of gas the velocities of all molecules are not same even their macroscopic parameters are fixed hence Maxwell introduced various speeds like

• Most probable speed-The speed which is attained by large no of molecules having value $v_{p} = 1.41\sqrt{\frac{kT}{m} }$

• Average speed- Average sum of all the speeds of molecules with value $v_{a} = 1.59\sqrt{\frac{kT}{m} }$

• Root mean squared - Value of this speed is $v_{rms} = 1.73\sqrt{\frac{kT}{M} }$

Thermal Expansion 

• A phenomenon in which substances expand on heating and contract on cooling with a change in their dimension is called Thermal Expansion. Depending on the shape of the body expansion is of three types

• Linear Expansion

• Area Expansion

• Volume Expansion

Thermal Expansion of Solids, Liquids, and Gases

• Thermal expansion is the phenomenon by which a material expands or contracts in response to changes in temperature. The formula for linear expansion of solids is given by:

ΔL = α * L * ΔT

Where:

ΔL = Change in length

α = Coefficient of linear expansion

L = Original length

ΔT = Change in temperature

• Similarly, for volume expansion in liquids and gases, the coefficients of volume expansion (β) and cubic expansion (γ) are used. The corresponding formulas are:

ΔV = β * V * ΔT (For liquids)

ΔV = γ * V * ΔT (For gases)

Calorimetry and Latent Heat

• Calorimetry involves the measurement of heat transfer during chemical reactions or physical processes. The specific heat capacity (C) of a substance is defined as the amount of heat required to raise the temperature of one gram of the substance by one degree Celsius. The formula for heat transfer (Q) is:

Q = m * C * ΔT

Where:

Q = Heat transfer

m = Mass

C = Specific heat capacity

ΔT = Change in temperature

• Latent heat is the heat absorbed or released during a phase change at constant temperature. The formula for latent heat (Q) is:

Q = m * L

Where:

Q = Latent heat

m = Mass

L = Latent heat of fusion or vaporization

Heat Conduction, Convection, and Radiation

• Heat conduction is the transfer of heat through a solid due to temperature differences. It is governed by Fourier's Law, which states:

Q = (k * A * ΔT) / d

Where:

Q = Heat transfer rate

k = Thermal conductivity

A = Cross-sectional area

ΔT = Temperature difference

d = Thickness

• Heat convection involves the transfer of heat through a fluid (liquid or gas) due to the motion of the fluid itself. It is described by Newton's Law of Cooling.

• Radiation is the transfer of heat through electromagnetic waves, and blackbody radiation laws, including Kirchhoff's law, Wien's displacement law, and Stefan's law, describe the behavior of ideal radiators.

Ideal Gas Laws

• For an ideal gas, the equation of state combines Boyle's Law, Charles's Law, and Avogadro's Law into the ideal gas law:

PV = nRT

Where:

P = Pressure

V = Volume

n = Number of moles

R = Ideal gas constant

T = Temperature (in Kelvin)

Blackbody Radiation

• Blackbody radiation laws describe the behavior of ideal radiators. These laws include absorptive and emissive powers, Kirchhoff's law, Wien's displacement law, and Stefan's law. They are crucial for understanding the thermal radiation of objects.

Isochoric Process

Isothermal Process

Adiabatic Process

Isobaric Process

This process takes place at const volume.

That process in which the temperature of the system is kept constant is called Isothermal process. 

This process doesn’t allow any exchange of heat i.e. the system is an insulated one with zero amount of heat absorbed or released.

That process in which pressure of the system is kept constant is called Isobaric process. 

For this process the work done in or by the system is zero.

Work done for this system is given by

$nRT\times 2.303\times\log{\dfrac{V_{2}}{V_{1}}}$

Work done for this system is given by

$\dfrac{nR(T_{1} - T_{2})}{\gamma -1}$

Work done by the system for this process is 

W =nR$(T_{2} - T_{1})$

Sl. No

Name of the Concept

Formulae

1. 

Newton’s Law of Cooling

$\dfrac{dT}{dt} = -k(T-T_{s})$

2.

First Law of Thermodynamics

$\triangle Q $ = $\triangle U$ + $\triangle W$

3.

Heat Capacity

S = $\dfrac{\triangle Q}{\triangle T}$

4.

Specific Heat Capacity

s = $\dfrac{S}{m}$ or $\dfrac{\triangle Q}{m \triangle T}$

5.

Efficiency of heat engine

$\eta = \dfrac{W}{Q_{1}}$

6.

Coefficient of Performance

$\alpha = \frac{1-\eta}{\eta}$

7.

Work done by Isochoric Process

For this process the work done in or by the system is zero.

8.

Work done by Isothermal Process

$nRT\times 2.303\times\log{\dfrac{V_{2}}{V_{1}}}$

9.

Work done by Isobaric Process

W =$nR(T_{2} - T_{1})$

10.

Work done by Adiabatic Process

$\dfrac{nR(T_{1} - T_{2})}{\gamma -1}$

11.

Carnot Engine’s Efficiency

$\eta = 1-\dfrac{T_{2}}{T_{1}}$

12.

Most probable speed

$v_{p} = 1.41\sqrt{\frac{kT}{m} }$

13.

Average speed

$v_{a} = 1.59\sqrt{\frac{kT}{m} }$

14.

Root mean squared 

$v_{rms} = 1.73\sqrt{\frac{kT}{M} }$

15.

Mean free path

$\lambda= \dfrac{1}{\sqrt{2}n\pi d^{2}}$

16.

Linear Expansion 

$\dfrac{\Delta l}{l}= \alpha_{l}\Delta T$

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