Coefficient of Performance (COP) of the refrigerator

• It is denoted by α.
• Mathematically given as :
  • α = Q₂/W
  • where Q₂ is the heat extracted from the cold reservoir
  • W is the work done on the system–the refrigerant
• α can be greater than 1
• Using Law of energy conservation :- Q₂+W=Q₁
• This implies W=Q2-Q1
• Therefore:-
• α =Q2/Q1-Q2
• W ≠ 0 then Q1-Q2 ≠0
• This implies α ≠infinite

Second law of Thermodynamics

There are 2 statements of second law of thermodynamics given by two scientists:

• Kelvin-Planck ∫Statement: – No process is possible whose result is the absorption of heat from a reservoir and the complete conversion of the heat into work.
• Clausius statement: – No process is possible whose result is the transfer of heat from a colder object to a hotter object.

Explanation of Kelvin-Planck Statement: It is always impossible that the total amount of heat which is supplied to system will get converted to work, and there will always be loss of heat. Complete conversion of heat into work is not possible.

Explanation of Clausius statement: – Transfer of heat from colder body to hotter body won’t take place until some external work is done on the system.

Reversible and Irreversible processes

Reversible Process

• A thermodynamic process is reversible if the process can be turned back such that the system and surroundings return to their original states, with no other change anywhere else in the universe.

• This means in the Reversible processes if a process starts from initial state then it goes to final state and then it can reversed back from final state to initial state.
• Examples:- Isothermal expansion and compression,  Electrolysis 
• A process is reversible if :-

1. It is quasi-static
2. No dissipative forces (that is no loss of heat by friction etc.).
3. Both initial and final states of the system are in thermodynamic equilibrium with each other.

Irreversible Process

• Irreversible processes are those that cannot be reversed.
• Two causes which give rise to irreversible processes
  • Irreversible processes takes place at a very fast rate.
  • Dissipative Effects.
• Examples:-Plastic deformation, Combustion, Diffusion, Falling of water from hill.

Carnot engine

• A Carnot engine is named after Carnot scientist.
• It is a reversible heat engine operating between two temperatures.
• It has a maximum efficiency which no other engine can have.

Cycle of processes in a Carnot engine

Basic Function of any heat engine is it will take heat Q₁ from a hot reservoir at temperature T₁ and give heat Q₂   to a cold reservoir at temperature T₂.

• As system is absorbing heat so it is isothermal expansion. Engine absorbs heat Q₁ at temperature T₁.
• An adiabatic process takes place inside the engine because of which there is increase in the temperature of the engine from T₁ to T₂ but no flow of heat.
• As system is releasing heat so it is isothermal contraction. Engine releases heat Q₂ at temperature T₂.
• An adiabatic process takes place again which changes the temperature of the system from T₂ to T₁.
• One cycle of Carnot engine will have Isothermal expansion then adiabatic process, and then isothermal contraction followed by adiabatic process.
• This will keep on repeating.

The efficiency of Carnot engine is given by:-

η = 1 – T₂/T₁

The graph below depicts the Carnot cycle for a heat engine with an ideal gas as the working substance.