Thermodynamics presentation 2

1. Why do we need to study thermodynamics?
Knowledge of thermodynamics is required to design any device involving the
interchange between heat and work, or the conversion of material to produce
heat (combustion).
Examples of practical thermodynamic devices:

2. 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.
System - identifies the subject of the analysis by defining a boundary
Surroundings - everything outside the system boundary.
As an example, consider an Internal Combustion (IC) Engine

3. Closed System - fixed non-changing mass of fluid within the system, i.e., no
mass transfer across the system boundary but can have energy exchange with the
surroundings. Example: piston-cylinder assembly
Isolated System - a system that does not interact at all with the surroundings, e.g.,
no heat transfer across system boundary
Open System (Control Volume) - fixed volume in space, mass and energy
exchange permitted across the system boundary.
Example: jet engine
System Properties – macroscopic characteristics of a system to which a numerical
value can be assigned at a given time without knowledge of the history of the
system, e.g., mass, volume, pressure
There are two types of properties:
Extensive – the property value for the system is the sum of the values of the parts
into which the system is divided (depends on the system size) e.g., mass, volume,
energy
Intensive – the property is independent of system size
(value may vary throughout the system), e.g., pressure, temperature

4. Units – SI used exclusively
Fundamental units:
Mass kilograms kg
Length meter m
Time seconds s
T temperature Celsius/Kelvin oC/oK
Derived units:
Force (F) Newton N
Pressure (P) Pascal Pa
Energy (E) Joule J
Newton’s Law states: Force = mass x acceleration
F = m ⋅ a
[N] = [kg] [m/s2] 1 N = 1 kg⋅m/s2
P = F / A
[Pa] [kg⋅m/s2] [m2] 1 Pa = 1 kg/m⋅s2
E = F ⋅ x
[J] = [kg⋅m/s2] [m] 1 J = 1 kg⋅m2/s2

5. 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
ρ
lim
→
=
V V

6. Properties of a Pure, Simple Substance
A pure substance is one of uniform and invariable chemical composition
For our purposes a simple substance is taken as one for which if the values of two
intensive properties are known all the other properties can be found,
e.g., u= f(T,P)
P-v-T Relationship
A material can exist in the
1. solid phase
2. liquid phase
3. vapor (gas) phase
4. a mixture of the phases at equilibrium,
e.g., melting, vaporization or sublimation
Through experiments it is known that temperature and specific volume can be
considered as independent and pressure determined as a function of these two: P= p(T,v)
The graph of such a function is a surface, the P-v-T surface.

7. P-v-T surface of a substance that contracts on freezing (common metals)
Note
Note the step decrease in specific volume (step increase in density) when
going from liquid to solid

8. P-v-T surface of a substance that expands on freezing (water)
Note the step increase in specific volume (step decrease in density) when
going from liquid to solid
3-D surface plot not very useful, more instructive to look at 2-D
projections

9. P-T plot for substance that expands on freezing
Only single-phase regions observed
Two-phase regions appear as lines (edge view)
Triple point represents edge view of the triple line where all three phases
co-exist

10. T-v plot for substance that expands on freezing (water)
Constant pressure lines are known as isobars
The critical point defines the maximum temperature, i.e., above the critical
temperature a liquid and vapor cannot co-exist at equilibrium

12. Second Law of Thermodynamics
It is an observed fact that certain processes can only proceed
spontaneously in one direction (hot coffee gets colder)
The following does not occur
Another example, connecting high pressure tank with a low pressure tank:
where PE is the final pressure

13. The evolution of the Second Law
The First Law of Thermodynamics is used to calculate end states of a system as
it evolves, it does not answer the following questions:
1) In what direction does a spontaneous process go
2) What is the maximum possible work
The Second Law of Thermodynamics starts with a simple principal concerning
the direction of heat flow and evolves into developing a new property called entropy (S)
Clausius Statement
It is impossible for a system to operate in such a way that the sole result is the transfer of
heat from a cold to a hot body
Kelvin Planck Statement
It is impossible for a system that operates in a cycle to generate work while transferring
heat with a single reservoir

14. Recall, a reservoir is a body that has so much thermal capacity that its temperature doesn’t
change when heat transfer occurs
To illustrate the equivalence of the two statements consider the following:
Connect two thermal reservoirs with high thermal conductivity metal and
assume Q1 heat flows from TC to TH which according to Clausius is not possible
Then place a heat engine between TH and TC that draws Q1 heat from the TH
reservoir and dumps Q2 heat to the TC reservoir
Then place a heat engine between TH and TC that draws Q1 heat from the TH
reservoir and dumps Q2 heat to the TC reservoir

15. This is equivalent to
This engine takes heat from one reservoir (Tc) to produce work 􀃆 this is not
possible according to K-P statement and thus demonstrating the equivalency of the two
statements
Heat Engines
Work can easily be converted to heat and other forms of energy, but converting
heat into work is not so easy
Converting heat into work requires a heat engine
Earliest heat engine operated on steam:
Process I - add steam into the piston-cylinder to raise the pressure above
atmospheric pressure and thus push the piston down
Process II - add water to condense the steam and lower the pressure below
atmospheric pressure so the piston is “pulled” back up

16. Thermal Efficiencies
Basic characteristics of heat engine are:
1) Receive heat, QH, from a high
temperature source
2) Convert part of this heat to work, W
3) Reject the remaining waste heat,
QC, to a low temperature sink
4) Operate on a cycle
These devices involve a working fluid to and from which heat is transferred
First Law applied to the heat engine cycle yields
The efficiency of the cycle is defined as

17. Maximum possible work corresponds to
Thermal efficiency is the ratio of the work done and the heat input, substituting for W
For an internal combustion (IC) engine heat is supplied by combustion QH and
heat rejected through the exhaust QC, typically the thermal efficiency of combustion is
around 30%
Other engine mechanical inefficiencies translate into an even lower overall
efficiency

18. Refrigerators
A refrigerator takes heat from a hot reservoir (hot room) and dumps it into a cooler
reservoir (cooler outdoors).
The refrigeration cycle is the opposite of the heat engine requiring work
input
Note: this is not inconsistent with Clausius’ statement because the heat transfer from the
cold to the hot reservoir is not spontaneous.
Applying First Law to the refrigeration cycle
Coefficient of performance (COP) β defined as
Typical values of β are 3-4

19. Reversible and Irreversible Processes
Have shown that no engine can have 100% efficiency, the question becomes what
is the maximum efficiency a heat engine can achieve?
The maximum efficiency will correspond to a cycle consisting of a series of idealized
reversible processes
A reversible process is one which the system and its surroundings can be returned
to their respective original states at the end of the reverse process
If the system and surroundings cannot be returned to their respective original states the
process is termed irreversible and the process is said to involve irreversibilities.
A process is internally reversible if no irreversibilities occur inside the system boundary,
irreversibilities may occur outside the system
The Carnot Cycle
The most efficient cycle is one consisting solely of ideal reversible processes. The
Carnot cycle is such a cycle and it provides an upper limit on the performance of a real cycle
operating between the same two thermal reservoirs.
Carnot cycle consists of the following 4 reversible processes:
12 Adiabatic compression
23 Isothermal expansion
34 Adiabatic expansion
41 Isothermal compression

20. Process 1-2 Reversible Adiabatic Compression:
- Gas is compressed very slowly (quasi-equilibrium) so pressure remains uniform throughout
the system
- Work done on the system:
- Heat transfer QH to the gas, temperature stays at TH

21. Process 2-3 Reversible Isothermal Expansion
- Gas expands slowly, gas cools but as soon as the temperature drops dT it obtains heat
from hot reservoir raising the temperature back to TH. Since temperature difference is
always dT heat transfer is reversible
- Work done by the system
- Heat transfer QH to the gas, temperature stays at TH
Process 3-4 Reversible Adiabatic Expansion:
- Gas expands very slowly (quasi-equilibrium) so pressure remains uniform throughout the
system
- Work done by the system:
Gas temperature decreases from TH to TC
Process 4-1 Reversible Isothermal Compression
- Work done on the system
- Heat transfer QC from the gas, temperature stays at TC

22. Carnot cycle on a P-v diagram
Net heat transfer per cycle = QH - QC

23. Carnot Refrigeration Cycle
The Carnot heat-engine cycle is composed of totally reversible processes. The reverse of the
heat engine cycle is the Carnot refrigeration cycle.
Heat is removed from the cold reservoir and heat is added to the hot reservoir.

24. Carnot Principles
1. The efficiency of an irreversible heat engine is always less than the efficiency of a
reversible one operating between the same two reservoirs.
2. The efficiencies of all reversible heat engines operating between the same two reservoirs
are the same.
Violation of either principle results in the violation of K-P
Example: Consider two heat engines operating between the same two reservoirs, one
reversible and the other irreversible, and each engine is supplied the same amount of heat QH

26. Kelvin Temperature Scale
Carnot Pr. #2 implies that the efficiency of a reversible cycle is independent of the
working fluid and depends only on the temperature of the reservoir ηR = g(TH,TC)
Consider three reversible engines A, B and D. Where A and D draw heat Q1 from the same
reservoir at T1
Engines A and B can be combined into one reversible engine C

27. For each engine we can state (Q4 = Q3)
Since left hand side (LHS) is independent of T2 the RHS must also be independent of T2
This condition is satisfied only if:
Lord Kelvin proposed taking φ(T) = T, so that

28. The thermal efficiency of a reversible heat engine is
The thermal efficiency of a reversible refrigerator is
This is known as the Carnot Efficiency, it represents the highest possible efficiency
for an engine operating between two reservoirs at TC and TH
Use reversible heat engine to measure temperature of an object at temperature T on
Kelvin scale by measuring QH and QC

29. Gas Power Cycles
Deal with systems that produce power in which the working fluid remains a gas throughout
the cycle, i.e., no change in phase.
Internal Combustion (IC) Engine
There are two types of reciprocating engines:
1) Spark ignition – Otto cycle
2) Compression – Diesel cycle
Terminology:

30. Four stroke Spark Ignition Engine: Cycle consists of four distinct strokes (processes)
A complete cycle (4 strokes) requires two revolutions of the crank shaft

31. A comprehensive study of IC engines requires consideration of the details of the air
intake, combustion, and exhaust processes (MECH 435 – 4th year elective)
Thermodynamic Air-Standard Analysis
Used to perform elementary analyses of IC engines.
Simplifications to the real cycle include:
1) Fixed amount of air (ideal gas) for working fluid
2) Combustion process replaced by constant volume heat addition with piston at TDC
3) Intake and exhaust not considered, cycle completed with constant volume heat removal
with piston at BDC
4) All processes considered internally reversible
Air-Standard Otto cycle
Process 1 2 Isentropic compression
Process 2  3 Constant volume heat addition
Process 3  4 Isentropic expansion
Process 4  1 Constant volume heat removal