Revision Notes: Thermodynamics | Physics for JEE Main & Advanced PDF Download

Introduction to Thermodynamics

• Thermodynamics is the branch of physics focused on the transformation of heat into other forms of energy and vice versa.
• It is a macroscopic science, dealing with bulk systems and not delving into the molecular constitution of matter.
• A thermodynamic system is defined as a collection of an extremely large number of atoms or molecules confined within certain boundaries.
• The system has specific values for pressure (P), volume (V), and temperature (T).

Thermal Equilibrium and Zeroth Law

Thermal Equilibrium

• A thermodynamic system is in an equilibrium state when macroscopic variables like pressure, volume, temperature, and mass composition remain constant over time.
• In thermal equilibrium, the temperatures of two systems are equal.

Zeroth Law of Thermodynamics

• This law establishes thermal equilibrium and introduces temperature as a key parameter for identifying equilibrium.
• The law states, "If two systems are in thermal equilibrium with a third system, then those two systems are in equilibrium with each other."

Heat, Work, and Internal Energy

Heat Transfer

• Energy transferred between a system and surroundings due to temperature difference.
• Occurs when the system and surroundings have different temperatures.

Work Done

• Work occurs when a system moves through a distance in the direction of applied force.
• Expressed as dW = P dV, where P is the gas pressure in the cylinder.

Internal Energy

• For a bulk system with numerous molecules, internal energy (U) is the sum of kinetic (Ek) and potential (Ep) energies.
• Internal energy (U=E_k+E_p) is due to molecular motion and configuration.
• Macroscopic variable dependent only on the system's state.
• Value depends solely on the system's given state, independent of the path taken to reach that state.

First Law of Thermodynamics

• Essentially the conservation of energy applied to any system.
• States that the total heat energy change in a system is the sum of internal energy change and work done.
• Mathematically expressed as dQ=dU+dW. 

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Heat Transfer in Systems

• When heat dQ is applied to a system, part is used to increase internal energy (dU) and part is used for external work (dW).

Specific Heat Capacities for Gases

• Specific heat capacity for gases varies based on the process or conditions of heat transfer.
• Two principal specific heat capacities for a gas
  • Specific heat capacity at constant volume (C_υ).
  • Specific heat capacity at constant pressure (C_p).

Relation between Specific Heats

• First Law establishes a relationship between the two principal specific heats of an ideal gas.
• Relation:C_p−C_υ=R, where C_p and C_υ are molar specific heats under constant pressure and constant volume conditions, respectively.

Specific Heat Capacities of Gases

• C_p>C_υ for a gas.
• Reason:At constant volume, all supplied heat raises the temperature, while at constant pressure, heat is used for temperature increase and work against external pressure.

Heat Transfer at Constant Volume

• When heat is supplied at constant volume (C_υ)
  • No work is done by the gas against external pressure.
  • All energy is used to raise gas temperature.

Heat Transfer at Constant Pressure

• When heat is supplied at constant pressure (C_p):
  • Volume increases.
  • Heat energy used for temperature increase and work against external pressure.

Difference in Specific Heats

• Difference (C_p−C_υ) is the thermal equivalent of work done during gas expansion against external pressure.

Expression for Relation between C_p and C_υ

• Let P, V, and T be initial pressure, volume, and absolute temperature of one mole of ideal gas.

Case (i): Heat Transfer at Constant Volume

• Heat (dQ) supplied, temperature increases to T+dT.

On the other hand, at constant pressure,

Now, for a mole of an ideal gas

Thermodynamic State Variables

• Parameters describing equilibrium states of a system.
• Examples:pressure, volume, temperature, mass, and composition for a gas.

Equation of State

• Represents the connection between a system's state variables.
• Example:Ideal gas equation - PV=μRT, where P is pressure, V is volume, μ is the number of moles, R is the gas constant, and T is temperature.

Extensive Variables

• Indicate the size of the system.
• Examples: Volume, mass, internal energy.

Intensive Variables

• Do not indicate the size of the system.
• Examples: Pressure, temperature, density.

Thermodynamic Processes

• Any change in the thermodynamic variables of a system.

Quasi-Static Processes

• Processes sufficiently slow, avoiding accelerated motion of piston and large temperature gradients.
• Small changes in pressure, volume, or temperature.

Isothermal Process

• Change in pressure and volume without altering the temperature.
• Involves free exchange of heat between the gas and surroundings.

Adiabatic Process

• No heat exchange between the gas and surroundings.

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Work Done in Isothermal Change

• The work done dW under isothermal change is involved.
• For adiabatic process, Q = 0
  From first law of Thermodynamics,

P-V Diagram and Reversible Processes

P-V Diagram

• Graph representing pressure variation with volume.
• Work done by the system equals the area under the P-V diagram.

Reversible Process

• Process can retrace, passing through the same states.
• If not reversible, it's irreversible.

Causes of Irreversibility

• Many processes lead to non-equilibrium states (e.g., free expansion, explosive reactions).
• Irreversibility often results from friction, viscosity, and dissipative effects.

Second Law of Thermodynamics

• Governs phenomena not allowed by the First Law.

Kelvin-Planck Statement

• No engine can operate in a cycle, extracting heat from a hot body, converting it entirely into work without any residual change.
• 100% conversion of heat into work is impossible.

Clausius Statement

• A self-acting machine in a cycle, without external energy, cannot transfer heat from a cold body to a hot body.
• Heat cannot spontaneously flow from a colder body to a hotter body.

Heat Engines and Carnot's Engine

Heat Engine

• Device facilitating a cyclic process converting heat to work.
• Components
  • Heat source
  • Heat sink
  • Working substance

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Carnot’s Engine

• Hypothetical engine using a cyclic/reversible process between two temperatures.
• Efficiency formula: η = 1 - T₂/T₁ (where T₁ is source temperature, T₂ is sink temperature).

Carnot’s Theorem

• No engine working between T₁ and T₂ can surpass Carnot engine's efficiency.
• Carnot engine's efficiency is independent of the working substance.

Refrigerators and Coefficient of Performance

Refrigeration Process

• Removal of heat from bodies colder than their surroundings.
• Device for this process is called a refrigerator.

Refrigerator Functionality

• Absorbs heat at low temperature.
• Rejects heat at higher temperature.
• External mechanical work is involved.
• Functions as a heat engine in reverse, termed as a heat pump.

Reverse Carnot Process

• Refrigerator operates in the reverse process of a Carnot engine.
• System extracts heat from a low-temperature sink (T₂) and transfers it to a high-temperature source (T₁).

Coefficient of Performance

• Represents the efficiency of the refrigerator.
• Involves the work done on the system.
• Functionality based on the reverse Carnot process

Important Table

Here is the summarised table: