Thermodynamics Terms

System and Surrounding: The path of Universe chosen for thermodynamic consideration is called a system.

The remaining portion of the universe, excluding the system, is called surrounding.

Universe = system + surrounding

A system usually consists of a definite amount of one or more substance and is separated from the surrounding by a real or imaginary boundary through which matter and energy can flow from the system to the surrounding or vice versa.

Open ,closed and isolated system

Open system: A system is said to be an open system if it can exchange both matter and energy with the surrounding.

For ex: If some water is kept in an open vessel or if some reaction is allowed to take place in an open vessel ,exchange of both matter and energy takes place between the system and surrounding.

Closed system: If a system can exchange only energy with the surrounding but not matter it is called a closed system.

For ex: If some water is placed in a closed metallic vessel or if some reactions is allowed to take place in a cylinder enclosed by a piston, then as the vessel is closed, no exchange of matter between the system and surrounding can take place.As the vessel has conducting walls, exchange of energy can take place between the system and the surrounding.

If the reaction is exothermic, heat is given by the system to the surrounding.

If the reaction is endothermic, heat is given by surrounding to the system.

If the reaction is accompanied by decrease in volume, mechanical work is done by the surrounding on the system.

If the reaction is accompanied by increase in volume, the mechanical work is done by the system on the surrounding.

Isolated system: If a system can neither exchange matter no energy with the surrounding, it is called an isolated system.

For Ex: If water is placed in a vessel which is closed as well as insulated, no exchange of matter or energy can take place between the system and the surrounding.

The State of the System

The state of a system means the condition of the system which is described in terms of certain observable properties such as temperature, pressure ,volume of the system.

If any of these properties of the system changes ,the system is said to be in different state i.e. the state of system changes.

These properties of a system are called state variables.

The first and the last State of a system are called the initial state and the final state.

State function

A physical quantity is said to be state function if its value depends only upon the state of the system and does not depend upon the path by which this state has been attained.

or

A physical quantity is said to be a state function if the change in its value during the process depends upon initial state and final state of the system and does not depend upon the path or route by which this change has been brought about.

For ex: Physical quantities which are state function include pressure ,volume, temperature ,internal energy enthalpy, entropy ,free energy  etc.

Path function in Thermodynamics

A thermodynamic property that depends on the path between the initial and final state is known as the path function. The path functions depend on the path taken or covered between two (initial and final) states. For example, work and heat. If different paths are chosen to reach from one point to another point, the work done will be different however you reach the same point in each case. So, work is not a state function as we cannot say that a system will have a specific amount of work at a specific state.

State Function

Path Function

It refers to a property whose value does not depend on the path followed to reach that value.

It is a property whose value depends on the path followed to reach that value.

They are also called point functions.

They are also called process functions.

It can be integrated using values of the initial and final state of a system.

They need multiple integrals and limits of integration for integrating the property of the system.

Value of state function remains the same regardless of the path or steps involved to reach that value.

Value of the path function will be different if a different path is taken to reach the final state.

Different paths give the same value

Different paths give different values

For example; entropy, mass, temperature, volume, etc.

Example; heat and mechanical work.

Macroscopic system and macroscopic properties

If a system contains a large number of chemical species i.e. atoms, ions or molecules, it is called macroscopic system.

Thermodynamic does not deal with the properties of the individual atoms and molecules but deals with the matter in bulk. Properties of the macroscopic systems like temperature, pressure, volume, density, melting point, boiling point are called macroscopic properties or thermodynamic properties.

Macroscopic properties are of two types:

An extensive property of a system is that which depends upon the amount of the substance present in the system like mass, volume and energy.

An intensive property of a system is that which is independent of the amount of the substance present in the system like temperature, pressure, density, concentration, viscosity, surface tension, refractive index etc.

Thermodynamic Equilibrium

A system is said to be in thermodynamic equilibrium if its macroscopic properties like temperature ,pressure do not change with time.

Thermodynamic process

A thermodynamic process is said to occur when the system changes from one state to another.

1) Isothermal process:

When a process is carried out in such a manner that the temperature remains constant throughout the process, it is called isothermal process. When such a process occur, heat can flow from the system to the surrounding and vice a Versa in order to keep the temperature of the system constant.

2) Adiabatic process:

When a process is carried out in such a manner that no heat can flow from the system to the surrounding or vice a versa i.e. the system is completely insulated from the surrounding, it is called adiabatic process.

3) Isochoric process

It is a process during which the volume of the system is kept constant.

4) Isobaric process

It is a process during which the pressure of the system is kept constant.

Reversible process

A process which is carried out infinitesimally slowly so that all changes occurring in the direct process can be exactly reversed and the system remains almost in a state of equilibrium with the surrounding at every stage of the process.

A process which is not carried out infinitesimally slowly so that the successive steps of the direct process cannot be retraced and any change in the external condition disturbs the equilibrium.

Terms

Explanation

System

Part of the universe under investigation.

Open System

A system which can exchange both energy and matter with its surroundings.

Closed System

A system which permits passage of energy but not mass, across its boundary.

Isolated system

A system which can neither exchange energy nor matter with its surrounding.

Surroundings

Part of the universe other than system, which can interact with it.

Boundary

Anything which separates system from surrounding.

State variables

The variables which are required to be defined in order to define state of any system i.e. pressure, volume, mass, temperature, surface area, etc.

State Functions

Property of system which depend only on the state of the system and not on the path.

Example: Pressure, volume, temperature, internal energy, enthalpy, entropy etc.

Intensive properties

Properties of a system which do not depend on mass of the system i.e. temperature, pressure, density, concentration,

Extensive properties

Properties of a system which depend on mass of the system i.e. volume, energy, enthalpy, entropy etc.

Process

Path along which state of a system changes.

Isothermal process

Process which takes place at constant temperature

Isobaric process

Process which takes place at constant pressure

Isochoric process

Process which takes place at constant volume.

Adiabatic process

Process during which transfer of heat cannot take place between system and surrounding.

Cyclic process

Process in which system comes back to its initial state after undergoing series of changes.

Reversible process

Process during which the system always departs infinitesimally from the state of equilibrium i.e. its direction can be reversed at any moment.

Irriversible Process

This type of process is fast and gets completed in a single step. This process cannot be reversed. All the natural processes are of this type

 

Internal Energy

Every substance has a specific amount of energy that is determined by factors like the chemical nature of the substance, temperature, and pressure. The term “intrinsic energy” or “internal energy” refers to this type of energy. The letter U is used to signify it (earlier it was represented by the symbol E). It is made up of the individual particles’ kinetic energy and potential energy. 

Translational energy, rational energy, vibrational energy, and other forms of kinetic energy emerge from the motion of its particles. Electronic energy, energy due to molecular interactions, nuclear energy, and other types of interactions between particles all contribute to potential energy. 

Although traditional thermodynamics is concerned with the macroscopic characteristics of materials, such as temperature, pressure, and volume, thermal energy is understood at the microscopic level as a rise in the kinetic energy of motion of the molecules that make up a substance. The translational kinetic energy of gas molecules, for example, is proportional to the temperature of the gas, the molecules can rotate around their centre of mass, and the constituent atoms can vibrate with respect to each other. 

Chemical energy is also stored in the bonds that hold molecules together, and weaker long-range interactions between molecules require even more energy. The total internal energy of a substance in a particular thermodynamic state is the sum of all these kinds of energy. A system’s total energy contains its internal energy as well as any external sources of energy, such as kinetic energy from the system’s overall motion, and gravitational potential energy from its elevation

Internal Energy as the State of System

A variety of thermodynamic characteristics, such as pressure, volume, temperature, internal energy, and enthalpy, can be used to define a thermodynamic system. These are grouped into two categories: state functions and path functions. A state function is a property of a system whose value is determined by the system’s initial and final states.  These types of functions explain a function’s equilibrium state and are unaffected by how the system got there. Internal energy, for example, is a state function that is independent of the path taken to change the system’s state.

It is a system’s overall energy. This consists of a number of components, including molecule translational kinetic energy, bond energy, electronic energy, and the intermolecular interaction energy of the system’s constituents’ particles, among others. Internal energy is affected by factors such as pressure, volume, and temperature. All of the variables in this list are state functions. Mass, volume, pressure, temperature, density, and entropy are all examples of state functions. Some factors are influenced by the amount of matter present. Intensive properties are factors that are independent of the amount of matter present. 

Density is an example. A state function is a property of a system that is dependent only on the system’s state and not on the process by which it is achieved. Internal energy is independent of the path used to get from one condition to the next. It depends on the system’s current state.

Since accurate values of different types of energies are stored in a system, such as translational, vibrational, rational, chemical, and so on, it is impossible to compute the absolute value of internal energy possessed by a substance. The difference between the internal energies of the two states can be used to calculate the change in the internal energy of a reaction.

Let’s denote the internal energies in states A and B as UA and UB, respectively. The difference in internal energy between the two states will be,

∆U=UB – UA

∆U is positive if the internal energy of the products is greater than the internal energy of the reactants.

This means that if Up > Ur, then ∆U =Up – Ur = positive.

If the internal energy of the products is smaller than the internal energy of the reactants, then ∆U will be negative.

This means that if Up < Ur, then ∆U =Up – Ur = negative

Conclusion

Thus we conclude that State functions depend only on the state of the system, not on the path used to get to that state. … Heat and work are not state functions. Work can’t be a state function because it is proportional to the distance an object is moved, which depends on the path used to go from the initial to the final state.

Change in Internal Energy by Doing Work 

Let us bring the change in the internal energy by doing work. 

Let the initial state of the system is state A and Temp. TA Internal energy = uA On doing’some mechanical work the new state is called state B and the temp. TB. It  is found to be 

TB > T

uB is the internal energy after change. 

Δu = uB – u

Change in Internal Energy by Transfer of Heat 

Internal energy of a system can be changed by the transfer of heat from the  surroundings to the system without doing work. 

Δu = q 

Where q is the heat absorbed by the system. It can be measured in terms of  temperature difference. 

q is +ve when heat is transferred from the surroundings to the system. q is -ve when  heat is transferred from system to surroundings. 

When change of state is done both by doing work and transfer of heat. Δu = q + w 

Work and heat

Heat (Q): 

  • Energy is exchanged between system and surround in the form of heat when they are at different temperatures.
  • Heat added to a system is given by a positive sign, whereas heat extracted from a  system is given negative sign.
  • It is an extensive property.
  • It is not a state function.

Work (W):

  • Work = Force × Displacement i.e. dW = Fdx
  • Work done on the system is given by positive sigh while work done by the system is given negative sign.
  • Mechanical Work or Pressure-Volume Work: work associated with change in volume of a system against an external pressure.

 

 

Work (W)

Heat (Q)

Interaction

Mechanical

Thermal

Requires

Force and Displacement

Temperature difference

Process

Macroscopic pushes and pulls

Microscopic collisions

Positive value

W > 0 when a gas is compressed. Energy is transferred into system.

Q > 0 when the environment is at a higher temperature than the system. Energy is transferred into system.

Negative value

W < 0 when a gas expands. Energy is transferred out of system.

Q < 0 when the system is at a higher temperature than the environment. Energy is transferred out of system.

Equilibrium

A system is in mechanical equilibrium when there is no net force or torque on it.

A system is in thermal equilibrium when it is at the same temperature as the environment.

 

The First Law Of Thermodynamics

The first law of thermodynamics can be captured in the following equation, which states that the energy of the universe is constant. Energy can be transferred from the system to its surroundings, or vice versa, but it can't be created or destroyed.

             

First Law of Thermodynamics: Euniv = Esys + Esurr = 0
 

A more useful form of the first law describes how energy is conserved. It says that the change in the internal energy of a system is equal to the sum of the heat gained or lost by the system and the work done by or on the system.

First Law of Thermodynamics: Esys = q + w

The sign convention for the relationship between the internal energy of a system and the heat gained or lost by the system can be understood by thinking about a concrete example, such as a beaker of water on a hot plate. When the hot plate is turned on, the system gains heat from its surroundings. As a result, both the temperature and the internal energy of the system increase, and  E is positive. When the hot plate is turned off, the water loses heat to its surroundings as it cools to room temperature, and  E is negative.

The relationship between internal energy and work can be understood by considering another concrete example: the tungsten filament inside a light bulb. When work is done on this system by driving an electric current through the tungsten wire, the system becomes hotter and E is therefore positive. (Eventually, the wire becomes hot enough to glow.) Conversely, E is negative when the system does work on its surroundings.

The sign conventions for heat, work, and internal energy are summarized in the figure below. The internal energy and temperature of a system decrease (E < 0) when the system either loses heat or does work on its surroundings. Conversely, the internal energy and temperature increase (E > 0) when the system gains heat from its surroundings or when the surroundings do work on the system.

                         

 

APPLICATIONS

Work

Work can be defined as the product of the force used to move an object times the distance the object is moved.

w = F x d 

Imagine a system that consists of a sample of ammonia trapped in a piston and cylinder, as shown in the figure below. Assume that the pressure of the gas pushing up on the piston just balances the weight of the piston, so that the volume of the gas is constant. Now assume that the gas decomposes to form nitrogen and hydrogen, increasing the number of gas particles in the container. If the temperature and pressure of the gas are held constant, this means that the volume of the gas must increase.

2 NH3(g  N2(g) + 3 H2(g)

The volume of the gas can increase by pushing the piston partway out of the cylinder. The amount of work done is equal to the product of the force exerted on the piston times the distance the piston is moved.

w = F x d

The pressure (P) the gas exerts on the piston is equal to the force (F) with which it pushes up on the piston divided by the surface area (A) of the piston.

Thus, the force exerted by the gas is equal to the product of its pressure times the surface area of the piston.

F = P x A

Substituting this expression into the equation defining work gives the following result.

w = (P x A) x d

The product of the area of the piston times the distance the piston moves is equal to the change that occurs in the volume of the system when the gas expands. By convention, the change in the volume is represented by the symbol V.

V = A x d

The magnitude of the work done when a gas expands is therefore equal to the product of the pressure of the gas times the change in the volume of the gas.

|w| = PV

Work (Pressure-volume Work) 

Let us consider a cylinder which contains one mole of an ideal gas in which a  frictionless piston is fitted.

Work Done in Isothermal and Reversible Expansion of Ideal Gas

Isothermal and Free Expansion of an Ideal Gas 

For isothermal expansion of an ideal gas into vacuum W = 0

Work Done in Isothermal and Reversible Expansion of  Ideal Gas 

Isothermal and Free Expansion of an Ideal Gas For isothermal expansion of an ideal gas into vacuum W =  0