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CARNOT ENGINE

  • A Carnot engine is a theoretical construct in thermodynamics that represents an idealized heat engine operating on the Carnot cycle.

  • The concept was introduced by French physicist

Nicolas Léonard Sadi Carnot in 1824

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  • It is a reversible engine model

FATHER OF THERMODYNAMICS

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CARNOT’S THEOREM

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  • Heat engines that are working between two heat reservoirs are less efficient than the Carnot heat engine that is operating between the same reservoirs.

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  • Maximum efficiency is given as:

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ISOTHERMAL PROCESS AND WORK DONE DURING AN ISOTHERMAL PROCESS

Isothermal Process

An isothermal process is a thermodynamic process in which the temperature (T) remains constant throughout the transformation. This means that the internal energy (U) of an ideal gas does not change because internal energy depends only on temperature.

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Since the temperature is constant, the heat energy supplied to the system is entirely converted into work done by the gas.

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Mathematically, for an ideal gas, the first law of thermodynamics states:

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Since dU=0 in an isothermal process, we get:

Work Done in an Isothermal Process

For an ideal gas, the work done (W) during an isothermal expansion or compression is

 

where:

  • W = Work done (Joules)
  • n = Number of moles of the gas,
  • R = Universal gas constant (8.314 J/mol·K),
  • T = Absolute temperature (Kelvin)
  • Vi = Initial volume of the gas
  • Vf = Final volume of the gas

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ADIABATIC PROCESS AND WORK DONE DURING AN ADIABATIC PROCESS

Adiabatic Process

An adiabatic process is a thermodynamic process in which no heat is exchanged between the system and its surroundings.

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From the first law of thermodynamics:

  • If work is done by the gas (expansion), the internal energy decreases, and the temperature drops.
  • If work is done on the gas (compression), the internal energy increases, and the temperature rises.

 

 

To find the work done (W),

 

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TEMPERATURE AND VOLUME RELATION IN ADIABATIC PROCESS

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IDEAL GAS VS REAL GAS

 

  • A real gas is an actual gas that does not perfectly follow the ideal gas law (PV=nRT), especially under high pressure and low temperature conditions. Real gases exhibit deviations due to intermolecular forces and finite molecular volume

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  • Internal energy of a real gas depends both on temperature and volume.

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CARNOT ENGINE - PARTS

SOURCE

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  • A hot reservoir of heat at a high temperature T1

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  • Supplies heat Q1 to the working substance (gas).

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INSULATED CYLINDER

  • Cylinder with non-conducting walls
  • It consist the working substance
  • It has a non-conducting piston

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SINK

  • A cold reservoir at a low temperature T2
  • The gas rejects heat Q2 to this reservoir during isothermal compression

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INSULATED WALLS

  • Perfectly insulated stand
  • Working substance can undergo adiabatic process with no heat transfer

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CARNOT CYCLE

 

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* Work is done by the gas - positive

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2

* Work is done on the gas - negative

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CARNOTS REFRIGERATOR

 

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ABSOLUTE ZERO OF TEMPERATURE

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Absolute zero is the lowest possible temperature at which all molecular motion theoretically stops. It is defined as 0 Kelvin (0 K), which is equivalent to:

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  • −273.15°C (degrees Celsius)
  • −459.67°F (degrees Fahrenheit)

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At absolute zero, a system has minimum possible energy, and the entropy of a perfect crystal reaches zero (according to the Third Law of Thermodynamics). However, in practice, absolute zero cannot be reached, only approached

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