Thermodynamics B.Sc. 1st Year

System and Surrounding

The part of universe which is under study is called system and the rest part of the universe is called surrounding. That means the universe is the combination of system and surrounding.

Types of System

Open System
The system which can exchange both heat and matter with the surrounding is called open system. Hot water in a beaker is an example of this system.
Closed System
The system which can exchange only heat but not matter with the surrounding is called closed system. Hot water in a sealed tube is an example of this system.
Isolated System
The system which can exchange neither energy nor matter with the surrounding is called Isolated system. Hot water in a thermos flask is an example of this system.

Thermodynamic Process

When a system changes itself from one to another state, the operation is called procss.
Isothermal Process
The process which takes place at constant temperature is called isothermal process.
             i.e. ΔT = O
Adiabatic Process
The process in which no heat change occurs is called adiabatic process.
             i.e. ΔQ = O
Isochoric Process
The process which takes place at constant volume is called isochoric process.
             i.e. ΔV = O
Isobaric Process
The process which takes place at constant pressure is called isobaric process.
             i.e. ΔP = O
Reversible Process
The process which takes place infinitesimally slowly and whose direction at any point can be reversed by applying an infinitesimal change in the state of the system is called reversible Process.
Irreversible Process
The process which takes place in one step and can not be reversed. This is a fast process.

Extensive and Intensive Properties

Properties which depend upon the amount of the substance present in the system are called extensive properties. Mas, Volume, Number of moles, Enthalpy, Entropy, Free energy etc are the example of extensive properties. These properties are additive. If mass of the gas is changed, the volume is also changed and so is the number of moles and their internal energy of the system.
Properties which don't depend upon the amount of the substance present in the system are called intensive properties. Temperature, Pressure, Boiling Point, Melting Point etc are the example of intensive properties. If temperature of a glass of water is 25^oC, then each and every drop of water in this glass has the temperatue of 25^oC. These properties are non additive.

Internal Energy

All forms of energy associated with a system is called internal energy or simply energy of the system (E).
This is expressed in Joule. This arises due to movement of molecules, arrangement of atoms in molecules, number of arrangement of electrons in atoms etc.
It is neither possible nor necessary to calculate the absolute value of internal energy of a system. It is a state function so depend only on the initial and final state of the system.

Heat Capacity:

The amount of heat required to change its temperature by one degree of a substance.
              Q = CΔT
         or, C = Q/ΔT

Molar Heat Capacity

The amount of heat required to change its temperature by one degree of one mole of a substance.

Heat Capacity at Constant Pressure

The amount of heat required to change its temperature by one degree of a substance at constant pressure.
Heat Capacity at Constant Volume: The amount of heat required to change its temperature by one degree of a substance at constant volume.

Relation between C_P and C_V

We know that
H = E + PV
or, H = E + RT (as PV = RT for one mole)
differentiating the above equation w.r.t T, we get-
dH/dT = dE/dT + R(dT/dT)
or, C_P = C_V + R
or, C_P − C_V = R

First law of Thermodynamics

It is also called energy conservation principle. According to this principle, energy can neither be created nor be destroyed, it can only be transfer or change fron one form to another form.
In other way-
Heat absorbed (Q) by the system is equal to change in internal energy (ΔE) plus work done by the system (−W).
Q = ΔE + (−W)
or, ΔE = Q + W

Limitations of First Law of Thermodynamics

First law does not indicate whether heat can flow from a cold body to a hot body or not.
First law does not specify that process is feasible or not.
Practically it is not possible to convert the heat energy into an equivalent amount of work.

Work done in Isothermal and Reversible Expansion

Let us consider 'n' moles of an ideal gas enclosed in a cylinder fitted with a frictionless, weightless and movable piston. Let P be the pressure of the gas and P-dP be the external pressure under which volume of the gas increased by dV, then work done in this expansion is
dw = −(P − dP)dV = − PdV (as dP.dV is very small).
For a infinite volume change from V₁ to V₂, the total work done during expansion-

where P₁ and P₂ are the initial and final pressure respectively.
Question: 3 moles mole of and ideal gas are expanded isothermally and reversibly from volume of 10 m³ to the volume 20 m³ at 300 K. Claculate the work done by the system. (Answer: 5.178 KJ)

Joule-Thomson Effect:

When a gas is allowed to expand from high to low pressure through a porous plug under adiabatic conditions, the gas gets cooled. The drop in temperature (dT) produced by fall in pressure (dP) under adiabatic condition is called J-T Effect. The fall in temperature is due to decrease in kinetic energy of the gas molecules. Since a portion of it is used up in overcoming the vander waal force of attraction existing among them during expansion. Since ideal gas has no such forces, therefore, there is no expenditure of energy in overcoming these forces during expansion.

Inversion Temperature

The temperature at which Joule - Thomson Coefficient becomes zero is called Inversion Temperature(T_i).
T_i = 2a/Rb

Joule Thomson Coefficient for Ideal and Real gas