Lenoir cycle | Working process | Thermal efficiency

The Lenoir cycle is a thermodynamic cycle that can be invented by Jean Joseph Etienne Lenoir in 1860 is often used to model a pulse jet engine. 

Process of Lenoir cycle :

All type of process individually done in a heat engine in Lenior cycle. 

The Lenoir cycle consists of four processes which are following below. 

• A constant-volume gas expansion process. From the diagram shown below the ideal gas in the system absorbs some amount of heat from the heat source at a high temperature and then expands thus the work was done on surroundings. 
• A reversible adiabatic gas expansion process. In this process, the system is thermally insulated. The gas expands continuously and does work on surrounding, which causes the system to cool to a lower temperature. 
• A reversible isothermal gas compression process. In this process, work has done surrounding gas and cause a loss of heat.
• A reversible adiabatic gas compression process. In this process, surrounding continue to do work to a gas, which causes the temperature to rise back to high temperature attain in the first process. 

Lenoir cycle PV and TS Diagram

The thermal efficiency of Lenoir cycle : 

Thermodynamically, the efficiency of Lenoir cycle is given by

ŋ_Lenoir = Work done by the system / Heat supplied to the system

Brayton cycle

The Brayton cycle is a thermodynamic cycle that can be invented by George Brayton in 1872.

The Brayton cycle is a type of power cycle that utilizes and ideal gas to generate power from a type of fuel used to heat the air.

What is the Brayton cycle?

In the Brayton cycle, two reversible adiabatic processes and two constant pressure process are done in a heat engine. 

Process of Brayton cycle :

The Brayton cycle consist of four processes following below :

• Adiabatic quasi-static process compression process: In this process compressor takes fresh ambient air and compressed it to a higher temperature and pressure. 
• Constant pressure heat addition process: In this process, compressed air is sent to the combustion chamber where fuel is burnt at constant pressure. 
• Adiabatic quasi-static expansion process: High-temperature gases expand to the ambient temperature in the turbine and produce the power.
• Constant pressure heat rejection process: The exhaust gases leave the turbine and air back to its initial condition.

The efficiency of the Brayton cycle :

In general, the thermal efficiency of the Brayton cycle is defined as the ratio of the work output to the heat input at the high temperature.

ŋ_th = W / Q_H

For ideal gas can now we expressed in terms of temperature :

ŋ_th  = NetWork / Heat Input = W_T – W_C / Q_in

      = c_p [ (T₃ – T₄ ) – (T₂ – T₁) ] / c_p (T₃ – T₂)

      = 1 – [ (T₄ – T₁) / (T₃ – T₂) ]

Where,

W_T = Work is done by the gas in the turbine

W_C = Work was done on the gas in the compressor

c_p = Heat capacity ratio 

Ericsson cycle

The Ericsson cycle is a thermodynamic cycle that can be invented by John Ericsson in 1840.

What is the Ericsson cycle?

In the Ericsson cycle, two isothermal processes and two constant pressure process are done in a heat engine. 

This cycle is mostly used in a closed cycle gas turbine. 

Process of Ericsson cycle :

The Ericsson cycle consist of four processes following below :

• A reversible isothermal gas expansion process is air as a working fluid which is heated from the heat addition process so work is done during this process.
• A constant pressure heat transfer or isobaric process is the air passed through the re-generator is released as exhaust gas. The heat absorbed by the re-generator is used during the next part of the cycle. 
• A reversible isothermal gas compression process is air is drawn into the engine is compressed and pressurized air drawn into the air storage sink.
• A constant pressure heat transfer is the compressed air at high pressure passe through the regenerator and absorbs the previously stored heat then flows to the piston and cylinder where it gets expands and produces the work.  

Efficiency of Ericsson cycle :

The efficiency of Ericsson cycle is given by :

                                         Ŋ_cycle = W_net / Q₁  =  T₁ – T₂ / T₁ 

Although the thermodynamic process of the Ericsson cycle differ from those of the Carnot cycle both cycles have the same value of the thermal efficiency when both are operating between its T₁ and T₂.

The Ericsson cycle doesn't have any practical application but is mainly used in a gas turbine employing a large number of stages with insulators, reheaters and heat exchangers.

Stirling cycle

The Stirling cycle is a thermodynamic cycle that can be invented by Robert Stirling in 1845.

What is the Stirling cycle?

In the Stirling cycle, two isothermal processes and two constant volume process are done in a heat engine. Constant volume process is performed with the help of a re-generator to make this cycle reversible.

Process of Stirling cycle :

The Stirling cycle consist of four processes following below :

• A reversible isothermal gas expansion process is heat addition process from the external source so work is done during this process.
• A constant volume heat transfer process is internal hear transfer takes place from the gas to the re-generator.  
• A reversible isothermal gas compression process is heat rejection to the external sink.
• A constant volume heat transfer is internal heat is transfer from the re-generator to a gas. 

The efficiency of the Stirling cycle :

The efficiency of the Stirling cycle is the same as that of the Carnot cycle. This is due to the fact that this cycle is also reversible as Carnot cycle. So remember that all reversible cycle have the same efficiency.

                                         Ŋ_cycle = W_net / Q₁  =  T₁ – T₂ / T₁ 

Also, the COP of the Stirling cycle and Carnot cycle are the same.

What is carnot cycle

The Carnot cycle is a thermodynamic cycle that can be invented by French Physicist Sadi Carnot in 1824.

What is the Carnot cycle?

In the Carnot cycle, two reversible isothermal processes and two reversible adiabatic processes are done in a heat engine.

Process of Carnot cycle :

The Carnot cycle consist of four processes following below :

• A reversible isothermal gas expansion process. From the diagram shown below the ideal gas in the system absorbs some amount of heat from the heat source at a high temperature and then expands thus the work was done on surroundings. 
• A reversible adiabatic gas expansion process. In this process, the system is thermally insulated. The gas expands continuously and does work on surrounding, which causes the system to cool to a lower temperature. 
• A reversible isothermal gas compression process. In this process, work has done surrounding gas and cause a loss of heat.
• A reversible adiabatic gas compression process. In this process, surrounding continue to do work to a gas, which causes the temperature to rise back to high temperature attain in the first process. 

The efficiency of the Carnot cycle :

It can be defined as the ratio of the energy output to the energy input. Here energy output is work done and energy input is heat addition.  

From the calculation,

Q₁ = Heat addition = R T₁ ln v₂ / v₁

W_net = R ln v₂ / v₁ (T₁ – T₂ )

Ŋ_cycle = W_net / Q₁  =  T₁ – T₂ / T₁

The large back work is a big drawback of this cycle. 

Assumption of the Carnot cycle :

• No friction at all between the piston and cylinder and also other moving parts of the engine, thus there is no heat generated and lost due to friction.
• There is no transfer of heat with the external atmosphere because the engine is completely insulated.
• There is also no exchange of heat between various parts of the engine.

What is rankine cycle

The Rankine cycle is the fundamental operating cycle of all power plants where an operating fluid is continuously evaporated and condensed. 

What is the Rankine cycle?

For each process in the vapour power cycle, it is possible to assume a hypothetical or ideal process which represents the basic intended operation and involves no extraneous effects. 

For the steam boiler, this would be a reversible constant pressure heating process of water to form steam.
For the turbine, the ideal process would be a reversible adiabatic expansion of steam. 
For the condenser, it would be a reversible constant pressure heat rejection as the steam condenses until it becomes saturated liquid. 
For the pump, the ideal process would be the reversible adiabatic compression of this liquid ending at the initial pressure. 

When all these four processes are ideal, the cycle is an ideal cycle, called the Rankine cycle.

The efficiency of the Rankine cycle :

Efficiency is the ratio between energy output to energy input. Here work done is energy output and energy input is heat addition. 

Net work is done = Work done in turbine + Work done in pump 

Net heat transfer = Heat produced in boiler + Heat rejected in the condenser 

ŋ = W_T - W_P / Q_S 

What is thermocouple

A thermocouple circuit made up from joining two wires of two dissimilar metals so due to the different effect net e.m.f is generated in the circuit which depends on the difference in temperature between the hot and the cold junctions.

This e.m.f can be measured by a microvoltmeter to a high degree of accuracy. The choice of selecting metal depends on the temperature range to be investigated, and copper constantan, chrome-alumni and platinum-rhodium are mostly used combinations. 

Advantages of a thermocouple are that it comes to thermal equilibrium with the system, whose temperature is to be measured, quite rapidly, because its mass is small.

Different effect to generate net e.m.f is :

• Seebeck effect 
• Peltier effect
• Thomson effect 

Electrical resistance thermometer

In the resistance thermometer, the change in resistance of a metal wire due to its change in temperature is the thermometric property. The wire, frequently platinum, may be incorporated in a Wheatstone bridge circuit. The platinum resistance thermometer measures temperature to a high degree of accuracy and sensitivity, which makes it suitable as a standard for the calibration of other thermometers.

In a restricted range, the following quadratic equation is often used :

R = R₀ ( 1 + At + Bt² )

Where,

R₀ = Resistance of platinum wire when it is surrounded by melting ice and A and B are constants.

Gas thermometer

To measure temperature, a reference body is used, and a certain physical characteristic of this body which changes with temperature is selected. 

The change in the selected characteristics is an indication of the change in temperature and selected characteristics are the thermometric property and reference body which is used is called thermometer.

All thermometers are working examples of the zeroth law of thermodynamics. 

Significance :

They used to calibrate other thermometers. 

Working principle and construction :

Constant pressure gas thermometer :

A small amount of gas is enclosed in bulb B which is in communication via the capillary tube C with one limb of the mercury manometer M. The other limb of the mercury manometer is open to the atmosphere and can be moved vertically to adjust the mercury levels so that the mercury just touches lip L of the capillary. The pressure in the bulb is used as a thermometric property and it is given by :

p = p₀ + ρ_M Z_g

Where,
p₀ = atmospheric pressure 
ρ_M = density of mercury

When the bulb is brought in contact with the system whose temperature is to be measured, the bulb, in course of time, comes in thermal equilibrium with the system.

The gas in the bulb expands, on being heated, pushing the mercury downward. The flexible limb of the manometer is then adjusted so that the mercury again touches the lip L. The difference in mercury level Z is recorded and the pressure p of the gas in the bulb is estimated. Since the volume of the trapped gas is constant, from the ideal gas equation, 

ΔT = V / R * Δp

The temperature increase is proportional to the pressure increase. 

Constant volume gas thermometer :

In a constant-pressure gas thermometer, the mercury levels have to be adjusted to keep Z constant, and the volume of gas V, which could vary with the temperature of the system, becomes the thermometric property. 

ΔT = V / R * ΔV

The temperature increase is proportional to the observed volume increase.

Constant volume gas thermometer is mostly use, since it is simpler in construction and easier to operate. 

Ideal gas

From the experimental observations p-v-T behaviour of the gases given by,

pṽ = ṜT

Where Ṝ is the universal gas constant value of  Ṝ is 8.3141 J / mol K

ṽ is the molar specific volume m³/gmol

Dividing upper equation by the molecular weight µ.

pv = RT

Where v is specific weight m³/gmol

R is the characteristic gas constant

We also get this the equation in terms of total volume V of gas, 

PV = nṜT

PV = mRT

Where n is the number of moles and m is the mass of the gas. An equation can be written for two states of the gas is 

P₁V₁ / T₁ = P₂V₂ / T₂

All equation is called the ideal gas equation of state. At very low pressure or density, all gases and vapours approach ideal gas behaviour.

Celsius temperature scale

The Celsius temperature scale employs a degree of the same magnitude as that of the ideal gas scale, but its zero points are shifted, so that the Celsius temperature of the triple point of water 0.01 degree Celsius or 0.01⁰C. 

If t denotes the Celsius temperature, then 

t = T - 273.15⁰ 

Thus the Celsius temperature ts at which steam condenses at 1-atmosphere pressure 

t_s = T_s - 273.15⁰ 

    = 373.15 - 273.15 = 100.00 ⁰C

Similar measurements for ice points show this temperature on the Celsius scale to be 

0.00 ⁰C.

Measurement of temperature

The temperature of a system determines that the system is in thermal equilibrium with other system or not? 

If a body is at 85⁰ C, it will be 85⁰ C, whether measured by mercury in glass thermometer, resistance thermometer or constant volume gas thermometer. 

If X is the thermometric property, let us arbitrarily choose for the temperature common to the thermometer and to all systems in thermal equilibrium with it the following linear function of X :

Θ(X)  = aX

Where, 

a = arbitrary constant 

Two temperatures on the linear X scale are to each other as the ratio of the corresponding X.

Zeroth law of thermodynamics

Zeroth law of thermodynamics is the basis of temperature measurement. The property which distinguishes thermodynamics from other sciences is temperature. 

One might say that temperature bears as important relation to thermodynamics as the force does to statics or velocity does to dynamics. 

When two bodies maintain at different temperatures are brought into contact, after some time they attain a common temperature and are then said to exist in thermal equilibrium.

Zeroth law of thermodynamics :

When a body A is in thermal equilibrium with a body B, and also separately with a body C, then B and C will be in thermal equilibrium with each other. 

Notes :

In order to obtain a quantitative measure of temperature, a reference body is used, and a certain physical characteristic of this body which changes with temperature is selected. 
The change in the selected characteristics may be taken as an indication of the change in temperature. The selected characteristics are called thermometric property, and the reference body which is used in the determination of temperature is called thermometer. 

There are five different kinds of thermometer used are following below :

1. Constant volume gas thermometer
2. Constant pressure gas thermometer 
3. Electrical resistance thermometer
4. Thermocouple 
5. Mercury in glass thermometer 

Specific heat and latent heat

What is the specific heat?

Specific heat is the amount of heat required to raise a unit mass of the substance through a unit rises in temperature. 

The symbol c will be used for specific heat. 

C = Q / m * Δt J / kg k 

Where, 

Q = The amount of heat transfer ( J )

m = Mass of the substance ( kg )

Δt = The rise in temperature ( K ) 

Since heat is not a property, so the specific heat is qualified with the process through which exchange of heat is made. 

The product of mass and specific heat ( mc ) is called the heat capacity of the substance. 

For gases, 

If the process is at constant pressure ( c_p ).

If the process is at constant volume ( c_v ).

For solids and liquids, 

The specific heat does not depend on the process. 

What is latent heat?

The amount of heat required to cause a phase change in a unit mass of a substance at constant pressure and temperature.

There are three phases in which matter can exist: solid, liquid, and vapour or gas.

The latent heat of fusion is the amount of heat transferred to melt a unit mass of solid into a liquid. 

OR

to freeze unit mass of liquid to solid. 

The latent heat of vaporization is the quantity of heat required to vaporize unit mass of liquid into vapour. 

OR

to condense unit mass of vapour into liquid. 

The latent heat of sublimation is the amount of heat transferred to convert unit mass of solid to vapour. 

Heat transfer

In this article, we will discuss the heat, heat transfer and different modes of heat transfer. Now, first of all, we check it out what is the heat ?

Heat is the quality of being hot OR Intensity of high temperature. 

Heat is defined as the form of energy that is transferred across a boundary by virtue of a temperature difference.  

The temperature difference is the potential or force and the heat transfer is called the flux.

The transfer of heat normally from a high-temperature object to a lower temperature object.

Heat transfer :

The heat is transferred between two bodies which are in direct contact is called conduction.

Heat may be transferred between two bodies separated by empty space or gases by the mechanism of radiation through electromagnetic waves.

The transfer of heat between the wall and a fluid system in motion is called convection. 

All the above are the modes of heat transfer. The direction of heat transfer is taken from high-temperature system to the low-temperature system.

Heat flow into the system is taken to be positive and heat flow out of a system is taken as negative.

For denote, heat transfer symbol is used is Q.

There is no heat crosses the boundary of the system this process is called adiabatic process.
Thus, an adiabatic process is one in which there is only work interaction between the system and its surrounding.

A wall which is impermeable to the flow of heat is called an adiabatic wall.
A wall which permits the flow of heat is called a diathermic wall.

The unit of heat is Joule in S.I Unit system.

The unit of heat transfer is kW or W.

Work transfer and Heat transfer

In this article, we will discuss the work transfer and heat transfer properties and also some similarities between both of them then the difference between them.

Points to remember regarding heat transfer and work transfer :

• Work and heat transfer both are energy interactions.
• The same effect in a closed system is about either by heat transfer or by work transfer. 
• Both heat transfer and work transfer are boundary phenomena.
• Heat transfer is one type of energy interaction and it is due to temperature difference. All other energy interactions may be termed as a work transfer.
• Heat or work is not a property of the system. It cannot be stored by the system. Both heat and work are energy in transit.
• Both heat and work are path functions and inexact differentials. 
• The magnitude of heat transfer or work transfer depends upon the path of the system that follows during the change of state.

Difference between heat transfer and work transfer :

Heat transfer is an interaction of energy between a system and its immediate surrounding due to temperature difference. 

Work transfer is the interaction of energy between a system and its immediate surrounding due to property difference other than temperature.

Work transfer in thermodynamics

A close system and its surroundings can interact in two ways :

• By work transfer 
• By heat transfer 

Both are those are called interactions and these bring about changes in the properties of the system. 

In thermodynamics mainly studies these energy interactions and the associated property changes of the system.

Work Transfer :

Work is one of the basic modes of energy transfer. In mechanics, the action of a force on a moving body is called work. A force is a means of transmitting an effect from one body to another. An effect of that certain distance can be performed by a body. The product of force and distance is the same to accomplish the same effect. 

What is work?

The work is done by a force as it acts upon a body moving in the direction of the force.

The action of a force through a distance is called mechanical work. The product of the force and distance moved parallel to the force is the magnitude of mechanical work.

W = F * d

In thermodynamics, work transfer is considered as occurring between the system and the surroundings.

Work is said to be done by a system if the sole effect on things external to the system can be reduced to the raising of a weight.

When work is done by a system, it is arbitrarily taken to be positive.

When work is done on a system, it is taken to be negative. 

The symbol used for work transfer is W.

The unit of work is N.m or Joule. 1 N.m = 1 Joule 

The rate at which work is done is called power.

There are various types of work transfer which can get involved between them. 

• pdV work
• Electrical work 
• Shaft work 
• Paddle-wheel work or Stirring work 
• Flow work 
• Work was done in stretching a wire
• Work was done in changing the area of a surface film
• The magnetization of a para-magnetic solid

Absolute entropy definition

Definition of Absolute Entropy :

Answer :

• The increase in entropy of a substance as it goes from a perfectly ordered crystalline form at 0 K temperature where its entropy considers as zero.

What is melting point

Melting Point :

The temperature at which a given solid will melt is called the melting point.

The melting point is also called Liquefaction point. 

The melting point of a solid is the temperature at which it changes state from solid to liquid at atmospheric pressure. 

In theory, the melting point of a solid should be the same as the freezing point of the liquid.

At the melting point, the solid and liquid phase exist in equilibrium.

What is freezing point

Freezing point :

The temperature at which a liquid turns into a solid when it is cooled is called freeing point.

In other word, Liquids have a characteristic temperature at which they turn into solids, known as their freezing point.

Freezing point is also called the crystallization point.