Thermodynamics subject, Study notes of Thermodynamics

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Engineering Thermodynamics

By

Dr.P.N.Kadiresh

Professor/Aerospace Engineering Dept.,

B.S.Abdur Rahman Crescent Institute of Science and Technology

CONTENTS

1. Basic Concepts and First Law of Thermodynamics
2. Second Law of Thermodynamics
3. Pure Substance and Vapour Power Cycle
4. Gas Power Cycles
5. Isentropic Flow Through Nozzle
6. Refrigeration and Air-conditioning
7. Air Compressor

Why do we need to study thermodynamics?

Knowledge of thermodynamics is required to design any device involving the between heat and work.

Examples of practical thermodynamic devices:

Thermal Power Plant

Rocket Nozzle

What is thermodynamics?

 The study of the relationship between work, heat, and energy.  Deals with the conversion of energy from one form to another.  Deals with the interaction of a system and it surroundings.

Chapter 1 - Introduction

Why do we need to study thermodynamics?

Knowledge of thermodynamics is required to design any device involving the

Examples of practical thermodynamic devices:

Air Conditioner

Turbojet Engine

The study of the relationship between work, heat, and energy. Deals with the conversion of energy from one form to another. Deals with the interaction of a system and it surroundings.

Introduction

Knowledge of thermodynamics is required to design any device involving the interchange

Air Conditioner

Turbojet Engine

Macroscopic and Microscopic viewpoint of Thermodynamics:

Macroscopic (or Classical Thermodynamics):  In this approach, a certain quantity of matter is considered, without taking into the account the events occurring at the molecular level.  In macroscopic thermodynamics, the properties of system are assigned to the system as a whole and that are based on observable, measurable quantities and these effects can be perceived by the human senses.  Example: A moving car.

Microscopic (or Statistical Thermodynamics):  From the microscopic view point, matter is composed of large number of small molecules and atoms.  Microscopic thermodynamics is concerned with the effects of action of many molecules and these effects cannot be perceived by the human senses.  Example: individual molecules present in the air.

Energy: Energy is a convenient generic term for “something” which is transferred in the doing of Work.

Energy of most interest:  potential energy (gravity or “spring”)  kinetic energy  chemical energy  internal energy

Above forms can “store” energy, whereas work can’t. It is only transient manifestation process of transferring energy. Heat can’t either; it is also only transient manifestation process of transferring energy. So heat and work are other forms of energies in transition.

System: Identifies the subject of the analysis by defining a boundary. Either “a region in space” or “a particular collection of matter” must be treated consistently.

Surroundings: Everything outside the system boundary.

 Change of State: When system interacts with another system or with surroundings, the system is said to be undergoing change of state.

 Path – Locus of change of state.

 Process – If path is specified, process can be defined (based on which property is held constant between initial state and end state). ………………………………………………. Process Property held Constant

---

isobaric pressure isothermal temperature isochoric volume isentropic entropy ………………………………………………....  Thermodynamic Equilibrium – A system that maintains thermal, mechanical, phase and chemical equilibriums is said to be in thermodynamic equilibrium.

 Quasi-static Process – When a process is carried out in such a way that the system passes through infinite number of equilibrium states. It is a sufficiently slow process in which, locus of all state points are equilibrium points. A quasi-static process is a hypothetical process and essentially a reversible process.

 Cyclic process - when a system in a given initial state goes through various processes and finally returns to its initial state, the system has undergone a cyclic process or cycle.

 Reversible process - it is defined as a process that, once having take place it can be reversed. In doing so, it leaves no change in the system or boundary.

 Irreversible process - a process that cannot return both the system and surrounding to their original conditions

 Adiabatic process - a process that has no heat transfer into or out of the system. It can be considered to be perfectly insulated.

 Isentropic process - a process where the entropy of the fluid remains constant.

 Polytropic process - when a gas undergoes a reversible process in which there is heat transfer. It is represented as PVn^ = constant.

 Throttling process - a process in which there is no change in enthalpy, no work is done and the process is adiabatic.

Property Definitions

In order to speak of an intrinsic property “at a point” we must treat matter as a continuum, i.e., matter is distributed continuously in space  In classical thermodynamics a point represents the smallest volume ‘V’ for which matter can be considered a continuum.  The value of the property represents an average over this volume ‘V’.

At any instant the density , ρ , at a point is defined as

 

 

  

lim 

V V

M

V

unit: kg/m 3

Mass , M , of the system with volume, V , is

  M  dM   V dV dV

dM  

Note: if ρ is uniform over the volume M = V

Specific volume , , defined as

 



1 unit: m^3 /kg

The pressure , P , at a point is defined as

P

F A A A

  (^) 

lim

units: 1 Pa = 1 N/m 2 1 standard atmosphere = 101,325 Pa 1 bar = 100,000 Pa = 100 kPa = 0.1 MPa

Absolute pressure , Pabs , measured relative to a perfect vacuum Gauge pressure , Pg , measured relative to the local atmospheric pressure, Patm.

 First Law of Thermodynamics: When any closed system is undergoing a cycle, the net work delivered by the system is proportional to the net heat transferred to the system,

i.e., (∑ ) (^) ∑ ∑ = ∑ − = 0 Where J is Joule’s of Mechanical equivalent of Heat With same units for Q & W; Net heat transfer = Net work.

=

 First Law corollary 1: There exists a property of a closed system such that a change in its value is equal to the difference between the heat supplied and the workdone during any change of state.

Proof: Let us consider 1-A-2 & 2-B-1 two processes constituting a cycle, 1-2-1. From FLTD, () (^) + () (^) = +

Simply, + = +

− = −( − )------------------------(1)

Let us imagine, the cycle 1-2-1 is completed though the process C instead of B.

Applying FLTD for the cycle 1-2-1, =

Comparing equation 1 & 2

Change (Q-W) is same for the process B or C, it is independent of path it followed, so it is a point function and a property. Thus based on FLTD, (dQ – dW) is a property, we call it as internal energy (in kJ) or (‘u’ – specific internal energy in kJ/kg)

 First Law corollary 2: If a system is isolated from its surroundings (i.e., Q = 0; W = 0) then its internal energy remains unchanged du = 0; u = const.

 Work Done in Vacuum Rupture of membrane allows the gas to expand into vacuum. The system boundary moves but no force resisting the movement = 0 (OR) = 0

 Perpetual Motion Machine of first kind (PMMI) A machine which produces work without absorbing energy from the surroundings is not possible. It must be true if First Law is true.

 Energy Transport by Heat and Work and the Classical Sign Convention Energy may cross the boundary of a closed system only by heat or work. Energy transfer across a system boundary due solely to the temperature difference between a system and its surroundings is called heat.

Heat and work are energy transport mechanisms between a system and its surroundings. The similarities between heat and work are as follows: a) Both are recognized at the boundaries of a system as they cross the boundaries. They are both boundary phenomena. b) Systems possess energy, but not heat or work. c) Both are associated with a process, not a state. Unlike properties, heat or work has no meaning at a state. d) Both are path functions (i.e., their magnitudes depends on the path followed during a process as well as the end states.

Since heat and work are path dependent functions, they have inexact differentials designated by the symbol, . The differentials of heat and work are expressed as Q and W. The integral of the differentials of heat and work over the process path gives the amount of heat or work transfer that occurred at the system boundary during a process.

(not ΔQ)

(not ΔW)

That is, the total heat transfer or work is obtained by following the process path and adding the differential amounts of heat (Q) or work (W) along the way. The integrals of Q and W are not Q 2 – Q 1 and W 2 – W 1 , respectively, which are meaningless since both heat and work are not properties and systems do not possess heat or work at a state.

Conduction : It is the mode of heat transfer particularly in solids. In this mode of heat transfer, the heat transfers from one atom to its neighbouring atom through molecular vibrations. Rate of heat transfer by conduction, ̇ is governed by Fourier Law of heat conduction: ̇ = − , Where k - thermal conductivity of the chosen material (W/mK). A – Area normal to the heat flow (m^2 ) dT/dx – Temperature gradient in the direction of heat flow (^0 C/m)

Convection: This mode of heat transfer particularly occurs in fluids in motion. That is in both liquids and gases that are in motion. This mode of heat transfer occurs due to the transfer of energy through the bulk mass. In detail whenever there is a temperature difference in a fluid, density difference occurs and motion of fluid starts as lower density fluid attempts to reach the top of the fluid. During this motion mass and energy transfer occurs thus heat transfer takes place.

Rate of heat transfer by convection, ̇ ̇ is governed by Newton’s Law of cooling, ̇̇ = ℎ , where h = Convective heat transfer coefficient (W/m^2 K).

Radiation: In this mode, heat transfer takes place via electromagnetic waves. Electromagnetic waves transport energy like other waves and travel at the speed of light. This is the mode by which we receive solar energy from the sun.

Rate of heat transfer by Radiation, ̇ ̇ is governed by Stefan-Boltzmann law, ̇̇ = (^ − ^ ) , where σ – Stefan-Boltzmann constant, 5.67x10-8^ W/m^2 K^4

 Ideal gas equation:

Equation of state is defined from Avogadro’s law, which states that, equal volumes of all gases, at the same temperature and pressure, have the same number of molecules".

For a given mass of an ideal gas, the volume and amount (moles) of the gas are directly proportional if the temperature and pressure are constant.

=

if p = 760 mm of Hg = 1.01325 bar; T = 273.15 K, it occupies 22.4 m^3 /kgmol

1.01325 10^ 22.

We know that ̅ =

where n = number of moles

So gas equation can be written as,

= ; where = m is the mass of the gas and μ is the molecular weight of the gas.

=

= (

)

 = where R is the characteristic gas constant.

 Enthalpy: It is a composite property. It is defined or sum of internal energy and flow energy. Enthalpy : = + Specific Enthalpy : ℎ = + From FLTD, = + = +

For constant pressure process = (ℎ − ℎ )

 Specific heat at Constant volume : (^) : Defined as the rate of change with temperature of the specific internal energy of the system when volume is held constant.

Heat transfer for constant pressure process {[] = ( − )}

[] = ℎ = ( − ) ℎ − ℎ = ( − )

 Ratio of specific heats: =

 Relationships between , , &

From FLTD, | We know that for perfect gas = = + ℎ = + ℎ = + +

For constant pressure process, ℎ = + ( ) + 0 ℎ = + () ℎ = +

÷

=

Where → ℎ

where

= 8.314 .

= ℎ .

 Thermodynamic work or pdv work:

Let us consider a piston-cylinder arrangement. A gas is enclosed in the cylinder at Position 1, the pressure, temperature and volume of gas in the cylinder is P,T & V, if the gas is allowed to expand to an elemental distance dl, the force acting on the surface of the piston is,

The pressure forces acting on the piston, = [ ∗ ]

Workdone by the expanding gas in the piston for elemental distance dl is, = Workdone by the gas from state 1 to 2, = ∫

Thus, the area under the process curve on a p-V diagram is equal to the workdone during a quasi-static process of a closed system.

 Property Relation Properties have unique values for any (equilibrium) state. Properties are state functions and independent of path or process.

= ^ − ^ is exact differential.

Similarly; (^) ∫ = ^ − but work, not a property, because it is not independent of process.

≠ ^ −

= ^ ( ) ^ ;^ It is an inexact differential.

 Work is a path function:

 Constant Temperature Process (Isothermal Process) = ∫ We know that gas equation, = When, =

. .̇ = = =

^ =^ ^ ^ ∫^

( ) (^) = ln

 Polytrophic Process

^ = ^ = ^ =  = ( ) (^) = (^) ∫ = ^ ∫

 ( ) (^) = ^ = ^ ^ ^

^ ^ − ^

 Property relations for different thermodynamic processes:

 Constant pressure process (Isobaric process, p 1 = p 2 )



 Constant volume process (Isochoric process, v 1 = v 2 )



 Constant temperature process (Isothermal process, T 1 = T 2 )



 For polytropic process ( ^ = )

^ = ^ 



(^) (^) =

(^) (^)

(^) (^) 

=

(^) (^)





(^) (^)

=

(^) (^)

(^) (^) ^

=



(^) (^) =

(^) (^)

(^) (^)

/

