Thermodynamics Theory Sample

INTRODUCTION

THERMODYNAMICS : -

Thermodynamics is the science of energy transfer &
its effect on physical properties of substance.

Some medium is required to convert heat to work or
work to heat.

Eg.:- In I.C. engine. we give heat as input to the air
due to which its temperature increases & then piston dose
work.

In refrigerator, Freon gas is used as medium.

MICROSCOPIC & MACROSCOPIC APPROACH

* In microscopic thermodynamics, the behavior of the gas
is described by summing up behavior of each molecule
(Statistical thermodynamics)
* In macroscopic thermodynamics, the behavior of gas is
described by the net effect of action of all the molecules
which can be perceived by human senses. (Classical
thermodynamics)

THERMODYNAMICS SYSTEM, SURROUNDING
AND BOUNDARY

* A thermodynamic system is defined as quantity of
matter or region in space upon which attention is
concentrated in the analysis of problem.
* Everything external to system is called surrounding or
environment.
* The plane which separates system & environment is
called Boundary.
* System & surrounding together comprise a Universe.

TYPES OF SYSTEM

i) Closed System : It is a system of fixed mass i.e. no
mass transfer. There may be energy transfer into or out of
the system.
Eg. Gas confined in piston cylinder arrangement

ii) Open System :- Both mass & energy transfer across
boundary .
Eg. : Turbine

iii) Isolated System:- There is no interaction of mass &
energy across boundary
Eg. :- Thermos flask.

CONTROL VOLUME & CONTROL SURFACE

For thermodynamic analysis of open System,
attention is focused on a certain volume in space to which
continuously mass goes in & from which continuously
mass comes out, is known as control volume bounded by
a surface called control surface.

Property :- A thermodynamic property refers to the
characteristics which can be used to describe the
condition or state of the system
Eg. :- Temperature, Pressure, chemical composition,
color, volume, energy etc.

Features :- 1) Measurable characteristics which describes
the system.
ii) Definite unique value at particular state.
iii) Does not depend on path followed by system.
iv) Differential is exact.

Two types :-
a) Intensive properties :- Independent of mass.
Eg. : Pressure, temperature, density, composition,
Viscosity, Thermal conductivity, electrical potential etc.
b) Extensive property : - dependent on mass
Eg. Energy, Enthalpy, entropy, volume etc.
.
Note :- Specific extensive properties are intensive
properties.
Eg. : - Sp. energy, Sp. Volume, Sp. Enthalpy, etc.

THERMODYNAMIC STATE,

PROCESSES & CYCLES

* When all the properties of a system has a definite value,
the system is said to exist in a definite state
* Any operation in which one or more properties of
system changes is called change of state
* The succession of states passed through during
change of state is called path
* When the path is completely specified, the change of
state is called Process.
* A thermodynamic cycle is defined as a series of state
changes such that the final state is identical with initial
state.

HOMOGENOUS & HETEROGENOUS SYSTEMS

* A quantity of matter which is homogenous
throughout in chemical composition & physical structure
is called phase.
* A system consisting of single phase is called
Homogenous system
* A system consisting more than one phase is
heterogeneous system.

THERMODYNAMIC EQUILLIBRIUM

When no change in macroscopic property is registered if
the system is isolated from its surrounding then system is
said to be in thermodynamic equilibrium.

If 3 equilibrium conditions are satisfied, system is in
thermodynamic equilibrium
a) Mechanical equilibrium :- No unbalanced forces
b) Chemical equilibrium :- No chemical reaction
c) Thermal equilibrium :- when the system existing in
mechanical & chemical equilibrium is separated from
surrounding by a diathermic wall, & if there is no
spontaneous change in its properties then the system is
said to exist in state of thermal equilibrium.

** When condition of any one of three type of
equilibrium. does not exists, system is said to be in non
equilibrium state.

QUASI – STATIC PROCESS

A process carried out in such a way that each point of the
path is in equilibrium is known as Quasi static or
reversible process. Infinite slowness is the characteristic
of quasi static process.

POINT FUNCTION & PATH FUNCTION

Those functions which depend only on initial & final
states and does not depend on path followed is called
point function.
Eg. i) : - All those function thermodynamic properties
(pressure, temperature, volume etc.)
which depends on path is called path function
Eg : - Heat, work etc.

Check for property : -

dp = Mdx + Mdy
is a thermodynamic property if its deferential is exact.

i.e.  M    N  y
 y   x 
  
 x

A differential is said to be exact if its integration
between two end states can be carried out without
requiring any information variation of variables.
Eg. : - i) pdv + vdp.

= d (pv)
Integrating
d(pv) = pv

 an exact differential & hence property of system

Eg. ii) pdv
d(pv) - requires relationship between P & V, so inexact
differential P & V, so inexact deferential

Eg. iii) V dp + P dv
T T

If differential is exact.

i.e. M   N 
y  x 
  y

 x

Then this is property

Compare with dp = Mdx + N dy

M  V  P , N = P = V
T R T R

M     v      P   0
y    T   v  R 
  v p  p

 x

N      P      P    0
x   p  T  p  V  
 y  P 
 v

M   N 
y  x 
  y

 x

 given function is exact differential & hence property
of system.

ZEROTH LAW OF THERMODYNAMICS

When two separate systems are individually in thermal
equilibrium with the third system, then the two systems
are in thermal equilibrium with each other.

Significance :- It gives us the concept of temperature &
defines the isotherm.

* if the series of states can be found on a system which
are in thermal equilibrium with one state of another
system then locus of all these state is called as isotherm
Thermometry :- Act of measuring temperature with
accuracy & precision The sensing element or device has
certain physical characteristics which changes with
change in value as a function of temperature is called
thermometric property and corresponding substance is
thermetric substance.

TYPES OF THERMOMETERS

i) Liquid in glass thermometer :
a) Mercury - high temperature measurement (upto 3000C)
b) Alcohol - Low temperature measurement (upto -
1110C)

ii) Gas thermometer : Expansion & contraction type

a) Constant pressure type :

V α T ; V1 = V2
T1 T2

b) Constant volume type :

P α T ; P1= P2
T1 T2

iii) Resistance thermometer : Function on the principle
of change in resistance with temperature

Rt = R0 ( 1 + At + Bt2)

R0 = Resistance at 00C
A, B = Constant
t = Temperature

Resistance thermometer function on wheat stone bridge
principle.

Here, P, Q & S are known resistance & R is unknown
resistance.

P  S
Q R

Or R1 = S.Q.
P.

Substituting value of Rt, t can be determined
(Resistance R is kept at a place whose temperature is to
be measured).

iv) Thermocouple : A thermocouple is manufactured by
joining two dissimilar metals belonging to thermoelectric
series. One is a higher order element & other is lower
order element & two junctions are formed. One junction
is kept at ice point & other is kept at the point whose
temperature is to be measured.

Due to difference in temperature, an emf is created
& this emf is related to temperature as

e = at + bt2
(It works on seeback effect principle).

V) Pyrometer : Works on principle of radiation. Used to
measure temperature of distant objects.

IDEAL GAS AND THEIR BEHAVIOUR

* An ideal gas has no intermolecular forces of attraction
or repulsion, does not change its phase during
thermodynamic process & obeys a set of common rules
governing change of properties. Relationship between P,
V & T given by.

f(P.V.T.) = 0 or P = f (V,T)

Ideal gas obeys the law

Pv = RT
Note : As P  0, & T  0 , the real gas approaches ideal
gas behavior.

At reduced pressure & elevated temperature the gas
molecules lie far apart & molecular force of attraction
between them tends to be small.
* Gas deviates from ideal behavior at high press, & low
temp. i.e. at high densities.
Note :- For real gas, sp. heats are found to vary with
temperature.
Perfect gas is a gas which is ideal & has const value of Cp
& Cv.

BASIC GAS LAWS

I) Boyles law :- At const temp

V 1
P

or PV = Const.

* Valid only at very low temperature pressure or at
moderately high temp

II) Charles law :-
V  T at const pressure

V  at P= C
or 

T

OR

or P  at V= C
C 

NOTE :- Gay lussac & Renault found that at const.
pressure change in volume of any perfect gas
corresponding to unit degree temp change is given by 1/2
73 of its volume at O0 C,
Let Vo = volume of gas at O0 C,
Vt = Volume of gas at t0 C.

V1 Vo 1 t
273


IDEAL GAS EQUATION

PV = n R T.
R R = Universal gas Const = 8.314 kj/mok
R R = R.M.
R = Characteristic gas const (KJ/kg k).
M = Molecular mass
PV = n M R T

or PV = m R T [ n M = m = moss of gas]

Cp - Cv = R

CP  
CV

Eg : - For O2’ Ro2 = 8.314 = 0.262 KJ/qk
32

For air R = 8.314 = 0.287 KJ/qk
28.96

VANDER WAALS EQUATION OF GAS

The concept of perfect gas Pv = RT based on following
assumptions :-
1) There is little or no attraction between molecules of
gas.
II) Volume occupied by molecules themselves is
negligibly small compared to volume of gas.

When pressure is very small & temperature very
high, this assumption is valid and real gas obeys ideal gas
equation But as pressure increases & also volume of
molecles become appreciable compared to total gas
volume. Vander waal introduced correction factor.

 P Va2  (V - b) = RT
 
 
 

* The coefficient a introduced to account for the existence
of mutual attraction between molecules. The term a/V2 is
called force of cohesion.

* The coefficient b was introduced to account for volumes
of molecules & is known as co-volume.
Note :- Real gases conform more closely with vander
waals equation of state. Not obeyed by real gas in all
ranges of press & temperature.

COMPRESSIBILITY FACTOR (Z)

Z  Volume Actual volume of the gas (PV= RT)
predicted by ideal gas eqution

Or

Z  V P  PV
RT / RT

Note :- i) Factor Z is dimensionless & becomes unity for
ideal gas at all press & temp
ii) Magnitude of Z for a given gas gives an indication of
extent of deviation of gas from ideal gas behavior.

COMPRESSIBILITY CHAT

I) As p  o , Z  1
This shows gas behave more or less like perfect gas

as pressure is reduced
II) If Z < 1  actual density is greater than predicted by
ideal gas equation

If Z > 1  actual density is less than predicted by
ideal gas equation

SPECIFIC HEAT AT CONST. (CP) &
CONST. VOLUME (Cv)

* Specific heat at const vol. (Cv) is defined as ratio of
change in internal energy to change in temp at const.
volume

Cv   du 
 dt 

vc

Or du = Cvdt.
Or dU = mCvdt.

* Cp is defined as ratio of change in enthalpy with respect
to temperature at const. Pressure

Cp   dh 
 
 dt  pc

Or dh = Cpdt.

Or dH = mCpdt.

* Enthalpy of a gas is defined as
h = u + Pv [PV = flow work]

or H = U + pV

Cp - Cv = R, Cp   or Cp =  Cv.
Cv

 Cv   R
1

Cp =  Cv

Cp  R
 1

 = 1.67 - For manoatomic gaser.
(Eg. He, Ar, Kr, Xe etc.)

 = 1.4 - For diatomic gaser. (Eg. H2, O2, N2 ect.)
 = 1.33 - For polyatemic gases or triatemic gases

(Eg. SO2, NO2, ect.)

If R= R ,
M

Cv = MCv=  R
1

Cp = MCp = Cp) = mas = R
 1

Cv & Cp are molar sp. Heats at const. Vol. & Const.
Pressure resp. (kJ/mo.k)

Note:- Value of  depends only on molecular structure of
gas i.e. whether gas is monatomic, diatomic or olyatomic.

* Value of cp & Cv depends only on  & R i.e. number of
atoms in molecule & molecular weight of gas. They one
independent of temp or press of gas.

Note : For real gas increases spand Cv with temperature
but the ratio Cp - Cv = R is constant .
*  = Cp / Cv decreases with temperature for real gas.

Degrees of Freedom.

The number of independent quantities, which must be
known for describing completely state of motion of body
is called “Degree of Freedom”

1) Monatomic gas : - (3 DOF)

2) Diatomic gas :- (5 DOF)

3) Triatomic gas :- (6 DOF)

Note :- Cp   1 2 (Here n = DOF)
Cv n