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THERMODYNAMICS

Chapter No. 04

Shri Swami Vivekanand Shikshan Sanstha, Kolhapur 2

4.1 Introduction

Thermodynamics is the branch of physics that deals with the concepts of heat & temperature & the inter-conversion of heat & other forms of energy. Understand nature of many fundamental interactions in universe Study of— Thermodynamic system Thermodynamic variables Thermodynamic processes & Laws

4.2 Thermal Equilibrium

When two objects are at the same temperature, they are in thermal equilibrium. Shri Swami VivekTanahndiSshikcshoannSancstehap, Ktolhiaspurused^ in^ Zeroth^ law^ of^ thermodynamics.^3

4.4 Heat , Internal Energy & Work

1) Internal Energy

Internal energy is defined as the energy associated with the random disordered motion of the molecules of a system. It is the total energy of the all atoms or molecules of substance. For, Monoatomic gas---translational kinetic energy Polyatomic gas --- translational , rotational & vibrational K.E. Liquids & solids -- potential energy due to intermolecular forces

2) Thermodynamic system & Thermodynamic process

Thermodynamic system

Thermodynamic system is a collection or group of objects that can form unit which may have ability to exchange energy with its surroundings. Shri Swami Vivekanand Shikshan Sanstha, Kolhapur 4

Thermodynamic systems can be classified on the basis of possible transfer of heat & matter to environment I) Open system- Freely allows exchange of energy & matter with its environment e.g. water boiling in a kettle II) Closed system- Does not allow the exchange of matter but allows energy to be transferred e.g. water boiling in a boiler III) Isolated system- Matter as well as heat can not be exchanged with its environment. e.g. thermos flask. 5 Shri Swami Vivekanand Shikshan Sanstha, Kolhapur 5

ii) If TS >TE , energy flows from the system , Q < 0 iii) If TS =TE , there is no transfer of energy takes place between system & environment ,Q = Shri Swami Vivekanand Shikshan Sanstha, Kolhapur 7

4.4.4) Change in Internal Energy of a System

To understand how this transfer of energy between a system & its environment is possible. Lets consider the following experiment. 8 Above fig.4.5 (a) shows a cylinder filled with some gas in it. This cylinder is with a movable , massless & frictionless piston at one end. Shri Sw T am h i Vi e vek g an a an s d Sh i i n ksh s an i S d an e stha t , h Ko e lhap c u y r linder is a system & rest is its environment. 9

The does some work on the gas in moving it through some distance, gas gains energy & its temperature increases. On the other hand , gas pushes the piston out, some work is done by gas ,it looses energy & its temperature decreases.

5. First Law of Thermodynamics : ( Work & Heat are realted )

The first law of thermodynamics gives the mathematical relation between heat & work.

1) First Law of Thermodynamics

Consider a very common thermodynamic system which consists of some quantity of ideal gas enclosed in a cylinder with a movable , massless & frictionless piston as shown in fig. ( 4.6) below 10 Shri Swami Vivekanand Shikshan Sanstha, Kolhapur 10

In this case , the gas inside the cylinder is the system & the cylinder along with the piston is its environment. Consider the work done by the system in increasing the volume of the cylinder. During expansion, as shown in fig. 4.6 (a) , gas molecules strikes the piston lose their momentum & exerts pressure on it , piston moves through finite distance. The gas does positive work on the piston. When the piston is pushed in , volume of gas decreases as shown in fig. 4.6 (b) the gas molecules striking it gain momentum from the piston. The gas does a negative work on the piston. Shri Swami Vivekanand Shikshan Sanstha, Kolhapur 11

• Shri Swami Vivekanand Shikshan Sanstha, Kolhapur

The quantities Q & W can be positive , negative or zero, therefore , ∆U can be positive, negative or zero. The above fig. 4.8 (a) shows the case when more heat is added to the system than the work done by it. The internal energy of the system increases, ( ∆U > 0 ). Shri Swami Vivekanand Shikshan Sanstha, Kolhapur 14

The above fig. 4.8 (c) shows the case when heat added to the system & the work done by it are the same. The internal energy of the system remains unchanged, ( ∆U = 0 ) In short, the first law of thermodynamics is thus a generalization of the law of conservation of energy. Shri Swami Vivekanand Shikshan Sanstha, Kolhapur 16

4.6 Thermodynamic state variables -

The systems temperature changes means the system gains or release heat, also it’s properties also changes, these Properties of systems or State variables are measurable/ observable properties at equilibrium. we use the term variable to describe system. for example- Pressure (p), Temperature (T), volume (V), mass(m) used to describe systems. These are also called as macroscopic variables. ⮚ Intensive and Extensive variables -

• Intensive - does not depends on size of system.
• Extensive – depends on size of system. Ex. Consider system in equilibrium , divide this system in two half, equal compartments. We observed that Pressure(p), temp(T), density (ρ) are same in both size of compartments doesn’t matter, this are intensive variables. The internal energy (U) and mass (m) also same in equal compartments but different in unequal compartments this are Extensive variables.

⮚ 4.6.2 Thermodynamic state variables and Equation of state. Every equilibrium state of thermodynamic system is completely described by specific values of state variables (macroscopic) for example-

• Equilibrium state of gas can described by its pressure, volume, temperature ,mass.
• In case of fuel in automobile engine it’s state described by state variables also need it’s composition to describe it’s state. ✔ The thermodynamic systems not always in state of equilibrium, such systems not described by state variables. Ex. When Inflated ball punctured, air inside expands to atmosphere this is not equilibrium state. Thermodynamic state variable describe equilibrium state of system, the various state variable are not always independent , they can mathematically related. This mathematical relation between state variable is called as equation of state. For example – for ideal gas pV = nRT Where p – Pressure V - volume T - Temperature n – number of moles of gas R – gas constant ✔ For fixed amount of gas i.e. for given ‘n’ , there are only two independent variables – p and V , or p and T , or V and T. 19

⮚ Graphical representation of equation of state

• Graphical representation of equation of state of system of a gas is called p – V diagram or curve.
• p – V curve of ideal gas at constant temperature is called isotherm.
• Real gas have complicated states of equations and so complicated p – V curves. ✔ p - V diagrams of systems equation of state – We consider a system of gas inside cylinder and piston (mass-less , movable, and friction-less) in system i. expand gas with varying pressure. ii. Compress gas with varying pressure. iii. Expand gas at constant pressure. 20