Thermodynamics

THERMODYNAMICS
Caminero, Windel L.
Misa, Mary Angeline A.
Definitions
of
Useful Informations
 Thermodynamics - is the branch of science that deals with energy, it’s conversion
from one form to another and the movement of energy from one
location to another.
- science that deals with heat and work, and properties of
substances that bear a relation to heat and work.
- derived from the Greek words “therme” which means heat and
“dynamis” which means strength, particularly applied to motion.
 Temperature – it is an indication or degree of hotness and coldness and therefore
a measure of intensity of heat.
 Pressure – it is the amount of force applied normal to a surface divided by
the area of that surface, also defined as the magnitude of the
normal force divided by the area over which the normal force
acts.
 Absolute Temperature – is the temperature measured from absolute zero.
 Absolute Zero - is the temperature at which the molecules stop moving.
 Temperature Interval – is the difference between two temperature readings from the
same scale, and the change in temperature through which body
is heated.
6 Temperature Scales
Celsius or Centigrade
Fahrenheit
Kelvin
Rankine
Reamur
Ligem
Relation Between Temperature Scales
 The absolute Pressure and Gage Pressure :
 Absolute Pressure – is the true pressure measured above a perfect vacuum
 Gage Pressure – is the pressure measured from the level of atmospheric pressure
by most pressure recording instrument like pressure gage and
open-ended manometer.
 Atmospheric Pressure – is the pressure obtained from barometric reading.
Where : Pabs = absolute pressure ATM = 101.325 Kpa

Pgage = gage pressure = 14.7 psi
Patm = atmospheric pressure = 1.032 kg/cm^2
= 29.92 in. Hg
= 760 mmHg = 760 torr
= 1atm
= 0 Kpag
= 0 psig
Note : Pgage is equal to negative when the pressure is vacuum.
The pressure in pefect vacuum is -101.325kpa
Basic Laws of Thermodynamics
 The First Law of Thermodynamics deals with law of conservation of energy. States
that energy can neither be created no destroyed ; it can only be transformed from
one form to another.
 Second Law of Thermodynamics states that whenever energy is transferred/
transformed, the level of energy cannot be conserved and some energy must be
permanently reduced to a lower level.
 The Third Law of Thermodynamics deals with the restriction of all physical systems to
the temperature regime that excludes absolute zero.
 The Zeroth law is the law concerning thermal equilibrium and is the basis for
temperature measurement. The law states that when two bodies, isolated from other
environment, are in thermal equilibrium with a third body, the two are in thermal
equilibrium with each other.
 Newton’s Second Law of Motion states that “the acceleration of a particular body is
directly proportional to the resultant force acting on it and inversely proportional to
its mass”. Acceleration is also the derivative of velocity of a body with respect to
time.
Law of Conservation of Mass
 Mass (m1) entering the system is equal to the sum of the

stored mass ( Δm) and the mass (m2) that leaves the
system.
m1 = m2 + Δ m
Δ m = m1 + m2
Steady Flow System
 Steady Flow Process – is a process that takes place in an open system in
which the quantity of matter within the system is constant.
m1 = m2
A1V1ρ1 = A2V2ρ2
Where:
A = cross – sectional area
V = velocity
ρ = density
Heat and Entropy
 Heat – is a form of energy associated with the kinetic random motion of
large number of molecules.
 Sensible Heat – is the heat needed to change the temperature of the body
without changing its phase.
 Qs = mCΔT
Where :
Qs = sensible heat
m = mass
ΔT = change in temperature
C = specific
Ideal Gas of Perfect Gas Law
 Is a theoretically ideal gas which strictly follows Boyle’s law and Charles’ law of
gasses.
PV = mRT ; PV = nRT

P = Pressure (in absolute) R = universal gas constant
V = Volume m = mass (in kg,gm and lb)
R = Gas Constant n = no. of moles
MW = molecular weight (in kg/kmol, gm/mol & lb/lb/mol

Boyle’s Law
 In a confined gas, if the absolute temperature is held constant, the volume
is inversely proportional to the absolute pressure.
PV = PV
1 1 2 2
Where :
P = Pressure
V= Volume
Charles’ Law
 In a confined gas, if the absolute pressure is help constant the volume is directly
proportional to the absolute temperature.
V1 V2
=
Where :
T1 T2
T = Temperature
V = Volume
General Gas Law
 Combined charles’ and boyle’s law, each one of these laws states how
one quantity varies with another if the third quantity remains unchanged,
but if the three quantities change simultaneously, it is necessary to combine
these laws in order to determine the final condition of the gas.
𝑃1𝑉1 𝑃2𝑉2
=
𝑇1 𝑇2
Where :
P = Pressure
V = Volume
T = Temperature
Avogadro’s Law
 At equal volume at the same temperature and pressure conditions, the
gases contain the same number of molecules.
𝑚1 𝑀1 𝑅1 𝑀1
= ; =
𝑚2 𝑀2 𝑅2 𝑀2
Where :
m1 & m2 = masses
M1 & M2 = Molecular Weights
R1 & R2 = Gas Constants
The Internal Energy, Enthalpy and
Entropy of an Ideal Gas
∆U = mCv ∆T
∆H = mCp ∆T
𝑇2
∆S = mC ln ( )
𝑇1
Processes of Ideal Gas
 Isobaric Process – is an internally reversible constant pressure process of a
working substance
 Isothermal Process – an internally reversible constant temperature process

of a working substance
 Isentropic Process – is an internally reversible constant entropy process of a

working substance. It is also known as a reversible adiabatic process.
• Adiabatic Process – is a reversible process in which there is no flow of heat
between a system and its surroundings.
 Polytropic Process – is an internally reversible process during which PV^n =

C; where n is a constant
Carnot cycle
 Carnot cycle is the most efficient thermodynamic cycle. It consists of two
isothermal and two isentropic processes.
 Process 1-2: Isentropic Expansion

 Process 2-3: Isothermal Compression
 Process 3-4: Isentropic Compression
 Process 4-1: Isothermal Expansion
Analysis of Carnot Cycle:
 Heat Added (Qa)

Qa= T1 (S1-S4)
 Heat rejected (Qr)

Qr= T2 (S2-S3)
Qr= T2 (S1-S4)
 Net Work or Work Done

Wnet= Qa - Qr
 Cycle efficiency:
𝑊𝑛𝑒𝑡 𝑄𝑟
e= = 1-𝑄𝑎
𝑄𝑎
 Heat-temperature relations:
𝑄𝑟 𝑇2
=
𝑄𝑎 𝑇1
 Problem 1:
A heat engine is operated between temperature limits of 1370˚C and 260˚C.
Engine is supplied with 14,142 Kj/kwh. Find the carnot cycle efficiency in percent.
Solution:
T1= 1370˚C + 273 = 1643 K
T2= 260˚C + 273 = 533 K
𝑇1 −𝑇2 1643 𝐾−533 𝐾

ec= =
𝑇1 1643 𝐾
ec= 67.56%
Internal Combustion Engine
 Otto cycle (Gasoline engine)

The ideal or air-standard cycle for spark-ignition engine, commonly known as
gaasoline engine.
Process 1-2: Isentropic Compression

Process 2-3: Isometric Heat Addition
Process 3-4: Isentropic Expansion
Process 4-1: Isometric Heat Rejection
Analysis of Otto Cycle:
 Heat Added (Qa)

Qa= mcv(T3-T2)
 Hear Rejected (Qr)

Qr= mcv(T1-T4)
 Net Work Done (Wnet)

Wnet= Qa-Qr
 Volume Displacement
Vd= V1-V2
 Cycle Efficiency (e)

𝑊𝑛𝑒𝑡
e=
𝑄𝑎
 Alternate Formula for efficiency

1
e=1-
𝑟𝑘 𝑘−1
 Compression Ration (rk)

𝑉1 𝑉4
rk=𝑉2 = 𝑉3
 Percentage clearance
1
c=𝑟𝑘−1
 Clearance Volume
Vc= cVD
 Mean Effective Pressure

𝑊𝑛𝑒𝑡
P m= 𝑉𝑑
Problem 1:
In an air standard Otto cycle, the clearance volume is 18% of the

displacement volume. Find the thermal efficiency.
Solution:
Find rk,
1+𝑐 1+0.18
rk= = = 𝒓𝒌 = 𝟔. 𝟓𝟓𝟔
𝑐 0.18
A= rk^k-1 , A=(6.556)^1.4-1 = 2.12

1 1
e=1-𝐴 , e= 1-2.12 = 0.53
Diesel Cycle
 Diesel cycle is an ideal or air-standard cycle for compression-ignition
engine (Diesel Engine). This cycle is a constant pressure combustion cycle
named after Rudolf Diesel.
Process 1-2: Isentropic Compression

Process 2-3: Isobaric Heat Addition
Process 3-4: Isentropic Expansion
Process 4-1: Isometric Heat Rejection
Analysis of Diesel Cycle
 Heat Added (Qa)
Qa= mcp(T2-T1)
 Heat Rejected (Qr)

Qr= mcv(T1-T4)
 Net work Done

Wnet= Qa-Qr
 Cycle Efficiency
𝑊𝑛𝑒𝑡
e= 𝑄𝑎
 Compression ratio
𝑉1
rk=𝑉2
 Expansion ration
𝑉4
re=
𝑉3
 Cut-off ratio
𝑉3
rc=
𝑉2

Thermodynamics

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THERMODYNAMICS

Where : Pabs = absolute pressure ATM = 101.325 Kpa

 Mass (m1) entering the system is equal to the sum of the

PV = mRT ; PV = nRT

MW = molecular weight (in kg/kmol, gm/mol & lb/lb/mol

 Isothermal Process – an internally reversible constant temperature process

 Isentropic Process – is an internally reversible constant entropy process of a

 Polytropic Process – is an internally reversible process during which PV^n =

 Process 1-2: Isentropic Expansion

 Heat Added (Qa)

 Heat rejected (Qr)

 Net Work or Work Done

𝑇1 −𝑇2 1643 𝐾−533 𝐾

 Otto cycle (Gasoline engine)

Process 1-2: Isentropic Compression

 Heat Added (Qa)

 Hear Rejected (Qr)

 Net Work Done (Wnet)

 Cycle Efficiency (e)

 Alternate Formula for efficiency

 Compression Ration (rk)

 Mean Effective Pressure

In an air standard Otto cycle, the clearance volume is 18% of the

A= rk^k-1 , A=(6.556)^1.4-1 = 2.12

Process 1-2: Isentropic Compression

 Heat Rejected (Qr)

 Net work Done

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