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अभ्यासक्रम

Overview: Thermodynamics

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Estimated time: 61 minutes
Maharashtra State Board: Class 12

Definition: Thermodynamics

Thermodynamics is the branch of physics that deals with the concepis of heat and temperature and the inter-conversion of heat and other forms of energy.

Maharashtra State Board: Class 12

Definition: Thermal Equilibrium

When two objects are at the same temperature, they are in thermal equilibrium.

Maharashtra State Board: Class 12

Law: Zeroth Law of Thermodynamics

''If two systems are each in· thermal equilibrium with a third system; they are also in thermai equilibrium. with each other".

Maharashtra State Board: Class 12

Definition: Internal Energy

Internal energy is defined as the energy associated with the random, disordered motion of the molecules of a system.

Maharashtra State Board: Class 12

Key Points: Thermodynamic Systems and Processes

  • A thermodynamic system is the part of the universe chosen for study.
  • Surroundings are everything outside the system; the boundary separates them.
  • An open system exchanges both heat (energy) and matter with its surroundings.
  • A closed system exchanges only heat, not matter.
  • An isolated system exchanges neither heat nor matter, and a thermodynamic process changes the system's P, V, or T.
Maharashtra State Board: Class 12

Key Points: Sign Convention for Heat

  • → Heat absorbed by the system
  • Q < 0 → Heat released by the system
  • Q = 0 → No heat transfer (thermal equilibrium)
Maharashtra State Board: Class 12

Law: First Law of Thermodynamics

The change in internal energy of a system is equal to the heat supplied to the system minus the work done by the system on its surroundings.

Mathematically:

ΔU = Q − W

The first law of thermodynamics is a statement of the law of conservation of energy for thermodynamic systems. It shows that energy can neither be created nor destroyed, but can only be transformed between heat, work, and internal energy.

Maharashtra State Board: Class 12

Key Points: Thermodynamic state variables

  • A state variable is any measurable property of a system in equilibrium, like pressure, volume, or temperature.
  • Intensive variables do not depend on size (pressure, temperature), whereas extensive variables do (mass, volume, internal energy).
  • A system is in thermodynamic equilibrium only when all types of equilibrium exist together.
  • Thermodynamic equilibrium requires uniform pressure, uniform temperature, and no chemical change in the system.
Maharashtra State Board: Class 12

Definition: Equation of State

The mathematical relation between the state variables of a system is called the equation of state.

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Formula: Work Done in Thermodynamic Process

W = ∫ p dV

Maharashtra State Board: Class 12

Definition: Thermodynamic Process

A thermodynamic process is a procedure by which the initial state of a system changes to its final state.

Maharashtra State Board: Class 12

Definition: Quasi-Static Process

Processes in which changes in the state variables of a system occur infinitesimally slowly are called quasi static systems.

Maharashtra State Board: Class 12

Definition: Path

When a thermodynamic system changes from its initial state to its final state, it passes through a senes of intermediate states. This series of intermediate states when plotted on a p - V diagram is called a path.

Maharashtra State Board: Class 12

Key Points: Thermodynamic Process

  • Work done by a system depends on the path taken between the initial and final states.
  • The same initial and final states can be reached through different intermediate states.
  • Heat transfer also depends on the path followed during the process.
  • In free expansion, no heat is exchanged, and no work is done, yet the final state can be the same as in other processes.
Maharashtra State Board: Class 12

Key Points: Reversible and Irreversible Processes

  • A reversible process can be reversed completely, and the system returns to its initial state without energy loss.
  • An irreversible process cannot be reversed exactly and usually involves energy loss due to friction or other dissipative forces.
  • Most natural processes are irreversible, whereas theoretical thermodynamic processes are often assumed to be slow, reversible, and to involve an ideal gas.
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Definition: lsothermal Process

A process in which change in pressure and volume takes place at a constant temperature is called an isothermal process or isothermal change.

Maharashtra State Board: Class 12

Formula: Isothermal Process

Q = W = nRTln\[\frac {V_f}{V_i}\]

Maharashtra State Board: Class 12

Definition: Isobaric process

It is a constant pressure process. Boiling water at constant pressure, normally - at atmospheric pressure; is an isobaric process.

Maharashtra State Board: Class 12

Formula: Isobaric process

Cp = Cv + R

Maharashtra State Board: Class 12

Formula: Isochoric Process

Q  = ΔU + W = ΔU = nCv ΔT

Maharashtra State Board: Class 12

Formula: Adiabatic Process

W = \[\frac{\left(p_{\mathrm{f}}V_{\mathrm{f}}-p_{\mathrm{i}}V_{\mathrm{i}}\right)}{\left(1-\gamma\right)}\]

Maharashtra State Board: Class 12

Definition: Cyclic Process

A thermodynamic process that returns a system to its initial state is a cyclic process.

Maharashtra State Board: Class 12

Definition: Heat Engines

Heat engines are devices that transform heat partly into work or mechanical energy. Heat engines work by using cyclic processes and involve thermodynamic changes.

Maharashtra State Board: Class 12

Formula: Heat Engine

\[\eta=\frac{W}{Q_{\mathrm{H}}}=1+\frac{Q_{\mathrm{C}}}{Q_{\mathrm{H}}}=1-\frac{|Q_{\mathrm{C}}|}{|Q_{\mathrm{H}}|}\]

Maharashtra State Board: Class 12

Definition: Refrigerators and Heat Pumps

Refrigerators and heat pumps are heat engines that work in backward direction. They convert mechanical work into heat.

Maharashtra State Board: Class 12

Key Points: Refrigerators and Heat Pumps

  • Refrigerators and heat pumps use work to move heat from a cold place to a hot place.
  • Heat cannot flow from cold to hot on its own; a compressor supplies the required work.
  • The refrigerant undergoes a cycle of expansion, heat absorption, compression, and heat rejection.
  • The heat supplied to the hot region exceeds the heat removed from the cold region because work is added.
  • A better system removes more heat from the cold region using less work.
Maharashtra State Board: Class 12

Definition: Refrigerator

Refrigeration is a process of cooling a space or substance of a system and/or to maintain its temperature below its ambient temperature. In simple words, refrigeration is artificial cooling.

Maharashtra State Board: Class 12

Formula: Coefficient of Performance (CoP) of a Refrigerator

K = \[\frac{\left|Q_{\mathrm{C}}\right|}{\left|W\right|}=\frac{\left|Q_{\mathrm{C}}\right|}{\left|Q_{\mathrm{C}}\right|-\left|Q_{\mathrm{H}}\right|}\]

Maharashtra State Board: Class 12

Formula: Coefficient of Performance (CoP) of a Air Conditioner

K = \[\frac{\left|Q_{\mathrm{C}}\right|}{\left|W\right|}=\frac{Ht}{Pt}=\frac{H}{P}\]

Maharashtra State Board: Class 12

Key Points: Limitations of First Law of Thermodynamics

  • The First Law states that heat and work are interchangeable, but it does not specify which processes are physically possible.
  • In practice, heat cannot completely convert into work; no heat engine can be 100% efficient.
  • The Second Law imposes limits on heat flow and engine efficiency; heat cannot flow from cold to hot spontaneously.
Maharashtra State Board: Class 12

Definition: Kelvin–Planck Statement

It is impossible to construct a heat engine that converts all the heat absorbed from a hot reservoir completely into work.

Maharashtra State Board: Class 12

Definition: Clausius Statement

Heat cannot flow from a colder body to a hotter body without external work being done.

Maharashtra State Board: Class 12

Formula: Carnot Heat Engine

\[\eta=\frac{W}{Q_{\mathrm{H}}}=1-\frac{\left|Q_{\mathrm{C}}\right|}{\left|Q_{\mathrm{H}}\right|}=1-\frac{T_{\mathrm{C}}}{T_{\mathrm{H}}}\]

Maharashtra State Board: Class 12

Formula: Coefficient of Performance (CoP) of a Carnot Refrigerator

\[K=\frac{T_{\mathrm{C}}}{T_{\mathrm{H}}-T_{\mathrm{C}}}\]

Maharashtra State Board: Class 12

Law: Second Law of Thermodynamics

"The Carnot engine is the most efficient heat engine. Also, all Carnot engines operating between the same two temperatures have the same efficiency, irrespective of the nature of the working substance".

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