Characteristic equation of a Gas, Universal gas constant

It is modified form of General gas equation.

if mass of gas is 1 KG then pv=RT

R = characteristic gas constant

Universal gas constant: 

In case of molecular weight where

Mass = Molecular weight*No. of molecules

where M= molecular weight of gas expressed in kg-mole, m= mass, n=  No. of molecules 

R= Characteristic gas constant,

Ru= Universal gas constant, where Ru= MR

then

p*v=n*Ru*T .

General gas equation

General gas equation:

In order  to deal to deal with all practical cases, the Boyle's  law and Charle's are combined together, which give us a general gas equation.

Therefore from all the above equation 

where C is a constant, whose value depends upon the mass and properties of the gas concerned.

The more useful form of the general gas equation is:

where 1,2 suffixes refer to different set of conditions.

Law of Perfect gases

Law of Perfect gases:

A perfect gas (or a ideal gas) may be defined as a state of a substance, whose evaporation from its liquid state is complete (means liquid is completely converted  into gas). It may be noted that if its evaporation is partial, the substance is called vapour. A vapour contains some particles of liquid in suspension. The behavior of super heated vapours is similar to that of a perfect gas.

The physical properties of a gas are controlled by the following three variables:

1. Pressure exerted by the gas
2. Volume occupied by the gas
3. Temperature of the gas

The behavior  of a perfect gas, undergoing any change in these three variables, is governed by the following laws:

1.Boyle's law: This law was formulated by Robert Boyle in 1662. It states, "The absolute pressure of a given mass of a perfect gas varies inversely as its volume, when the temperature remains constant". mathematically .i.e, Pressure is inversely proportional to volume.

2.Charles law: This law was formulated by a Frenchman Jacques A.C. Charles in  about 1787. It states that volume is directly proportional to temperature.

3.Gay-Lussac law: This law states that Pressure is directly proportional to temperature.

Thermodynamic work

Thermodynamic Work:

Work is said to be done if the sole effect on the things can be reduced in raising of weight (weight may not be raised). for example imagine a cylinder with piston of weight 'W', when heat is transferred into the cylinder the pressure inside the cylinder increases there by lifting the piston to some height where heat energy is transformed to work.

Sign convention:

• Work done by the system is positive.
• Work done on the system is negative.

Remember:

• Work is not a property.
• Work is inexact differential.

How thermodynamic work is calculated ?

For Closed system:

For  closed system  the net amount of work done is equal to area under the curve of path between points A and B. The closed system work is obtained by plotting it on volume axis.
For Open system:

For  open system  the net amount of work done is equal to area towards the left side of the curve of path AB and vertical axis of P-V diagram. The open system work is obtained by plotting it on  pressure axis.

System, Process vs Cycle

Thermodynamic System and Surroundings:

System: A system is a matter or region on which analysis is done. 

Surrounding: Everything external to the system where either energy nor mass transaction takes place is known as surrounding.

Boundary: It separate both system and surroundings. it can be fixed or movable.

Fixed Boundary: e.g.rigid box containing gas

Movable boundary: e.g. Cylinder with piston. 

Types of system:

Types of system	Mass transfer	Energy transfer	Example
Closed system	No	Yes	Piston cylinder without valves
Open system	Yes	Yes	Turbine, pump, compressor.
Isolated	No	No	Universe, Hot coffee in a perfectly isolated thermos

Process:

A thermodynamic process is a change from one equilibrium state to another.

process can be classified into Reversible and Irreversible processes

Reversible process: A process is said to be reversible when reversed in direction it follows the same path as earlier.

Irreversible process: A process is Irreversible because when reversed in direction it doesn't follows the same path. 

Cycle:

A cycle is a series of processes forming a closed path whose initial and final points are same.

Similarly a cycle is classified of Reversible and Irreversible cycle.

Reversible cycle: If every process of a cycle is a reversible then the system undergoes a reversible cycle.

Irreversible cycle: Even if a single process is irreversible then the system runs on a irreversible cycle.

 Remember: A process can have 100% efficiency but in a cycle 100% efficiency is not possible .

for example water in a Pot can become cool without any external force applied. but for a refrigerator 

as it undergoes a cycle an external force(electricity) is applied for cooling.

Thermometric property and temperature measurement

Thermometric property:

It is a physical property that varies continuously with temperature.

Thermometric properties can be used to measure the temperature. 

For example imagine a closed constant volume(no change in dimension) tube on a heater, as the temperature increases the  pressure also increases. later when you remove the tube temperature decreases steadily with decrease in pressure inside the tube. here as the temperature is varying with pressure, by measuring the pressure and by applying the value in ideal gas equation we can find value of temperature. As the temperature is measured with the help of pressure, pressure is considered as the Thermometric property.

similarly below are few thermometric properties for respective thermometers.

Type of thermometer	Principle	Thermometric property
Resistance	Wheat stone bridge	Resistance
Thermocouple	See back effect	E.M.F
Constant volume gas thermometer	Ideal gas equation (PV=MRT)	Pressure
Constant pressure gas thermometer	Ideal gas equation (PV=MRT)	Volume

for mercury thermometer length is considered to be thermometric property.

Method of temperature measurement

method used before 1954:

T=[100(P-Pi)] / (Ps-Pi) 

here T= temperature

P= pressure corresponding to temperature T
Pi= pressure corresponding to ice point (273K)
Ps= pressure corresponding to steam point (373K)

Using Ice point & Boiling point of water the thermometer can be calibrated.

method  after 1954:

T=273.16(P/Ptp)where T=temperature,P= Property(volume or pressure) corresponding to temperature T,Ptp= Property(volume or pressure) corresponding to triple point temperature.

Using concept of Triple point. As the temperature and pressure at triple point are known. 

Triple point of water:

It is the point where all the phases (gas,liquid,solid) coexist. for water its value is 273.16K or 0.01 degree centigrade.

zeroth law of thermodynamics

Zeroth law of thermodynamics: zeroth law of thermodynamics is on the basis of temperature measurement.

Zeroth law states that if two bodies are in thermal equilibrium with a third body  then they’re in thermal equilibrium with each other.

From the above image if A is connected to B and are in thermal equilibrium with each other and body B is connected to C and are in thermal equilibrium with each other then both A and C are in thermal equilibrium with each other. 

Thermal equilibrium:

when there are variations in temperature from point to point of an isolated system, the temperature at every point first changes with time. This rate of change decreases and eventually stops. When no further changes are observed, the system is said to be in thermal equilibrium.

Why it is named  Zeroth law?

It is called the "zeroth" law because it was observed (as it is a observation) to light after the first and second laws of thermodynamics, but as it was considered more fundamental and a base for other laws of thermodynamics it was given a lower number "zero".

Application of zeroth law of thermodynamics:

The very basic use of zeroth law is used to compare & measure temperature.

This law is used to measure temperature & also to calibrate thermometer.

Laws of thermodynamics

Laws of thermodynamics:

There are actually four laws of thermodynamics. These laws are very important and are considered in every aspect of engineering related to thermodynamics and it's applications. These laws are on the basis of every day life and many modern technologies are based on these applications.

Zeroth law of thermodynamics: 

 Zeroth law states that if two bodies are in thermal equilibrium with a third body  then they’re in thermal equilibrium with each other.

From the above image if A is connected to B and are in thermal equilibrium with each other and body B is connected to C and are in thermal equilibrium with each other then both A and C are in thermal equilibrium with each other. 

First law of thermodynamics:

This law is also stated as Conservation law of energy.

This law states that the heat and mechanical work are mutually convertible. According to this law a definite amount of heat is converted to a definite amount of  work and loss of heat due to increase in internal energy and overcome friction losses and vice versa.

This law states that energy can neither be created nor destroyed. Though it can be transformed from one form to another. According to this law, the energy due to heat supplied(Q) must be balanced by the external work done(W) plus the gain in internal energy (E) due to rise in temperature. In other words 

Q = W + E

Second law thermodynamics:

This law is also stated as law of degradation energy .

This law states that there is a definite limit to the amount of mechanical energy, which can be obtained from a given quantity of heat energy. 

According to clausius this law states that "It is impossible to transfer heat from body at lower temperature to a body at a higher temperature without the aid of an external energy for a self acting machine in a work process." 

According to Kelvin plank this law states that "It is impossible to construct a engine whose sole purpose is to convert heat energy into work." Extracting heat and using it all do work would constitute an ideal engine which is forbidden by second law of thermodynamics.

Third law of thermodynamics:

This law states that entropy of a system remains constant when the system attains zero Kelvin or absolute zero(0K or -273C).

Thermodynamics process and cycle

Process 

Change of state is known as process.

Processes are classified into two types 

1. Reversible process: A process when reversed in direction follows the same path that of the forward path without leaving any effect on the system and surroundings.
   
2. Irreversible process: A process when reversed in direction doesn't follow the same path that of forward path by leaving traces of its effect on the system and surroundings. A process which is not reversible is known as irreversible process.
   

(imagine and feel while reading so that you can understand the concept)

Cycle

A system is said to have undergone a cycle when the initial and final points are same. For a cycle change in property is zero. A cycle is classified into reversible and irreversible cycle.

1. Reversible cycle: A cycle is said to be reversible if each and every process of the cycle is reversible. Reversible cycle is possible only in case of friction less quasi static process.i.e., a slow steady friction less process. There are no losses in a reversible cycle. Imagine a reversible adiabatic system where consider a insulated(no heat transfer takes place between cylinder and surroundings and is a slow friction less process ) cylinder with piston when compressed air inside the cylinder gets heated and when expanded the temperature decreases steadily and reaches to the original point. Here in this cycle initial and final points are same without effecting the surroundings.
2. Irreversible cycle: Even if single process is irreversible then it is said to be irreversible cycle. There are losses due to  friction, heat transfer. For example internal combustion engine where heat transfer takes place between cylinder and surroundings continuously. 

Thermodynamics equilibrium and properties of a system

Thermodynamics equilibrium 

A body is said to be in a thermodynamics equilibrium if it is in 

1. Thermal equilibrium: Equality of temperature 
2. Mechanical equilibrium: Equality of force and couples.
3. Chemical equilibrium: Equality of chemical potentials.

Properties of a system 

Properties are point functions and are exact or perfect differential. 

Properties are not path functions 

From the above graph 

A and B are the two paths between points 1 and 2.

Properties are of two types 

1. Extensive properties: These properties are dependent on mass. e.g. volume, energy, heat capacity, enthalpy. For example volume=(mass) / (density). Where volume is dependent on mass. Similarly energy unit is joule where Joule=(Kg*m^2)/sec where Kg is mass which plays an important role in value of energy.
2. Intensive properties: These properties are independent on mass. e.g. pressure, temperature, density, specific volume, specific heat, specific enthalpy. For example pressure is not dependent on mass. Same pressure can be obtained for different masses at different volumes. Temperature can be same for different masses. 

• Specific properties: specific properties are extensive properties per unit mass. Specific properties are intensive properties whose mass is cancelled.  For example specific volume= (volume) / (mass) where volume is denoted by capital 'V' and specific volume is denoted by small 'v'. And specific enthalpy=(enthalpy)/(mass) where enthalpy is denoted by 'H' and specific enthalpy is denoted 'h'. 

Point functions: Does not depend on path history (Temperature, pressure, volume). These properties are measured at a particular point of the system. 

Path functions : Depends on path history (work, heat). Because work is said to be done if it changes from one state to other state.

Thermodynamics system

Thermodynamic system 

System and surrounding:

• A system is a matter or region on which analysis is done.
• Everything external to the system is called surrounding.

System + Surrounding = "Universe"

Boundary:

• It separates system and surroundings.
• It can be fixed or movable.
• Fixed boundary ex: cylinder containing gas
• Movable boundary ex : cylinder with piston