Thermodynamics 1

Precious Arlene Villaroza-Melendrez

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 Table of Contents

Module 8: Processes of Ideal Gases 57

Introduction 57
Learning Objectives 57
Lesson 1. Constant Volume Process 57
Lesson 2. Constant Pressure Process 60
Lesson 3. Constant Temperature Process 63
Assessment 8 65
Summary 65

Module 9: Processes of Ideal Gases 67

Introduction 67
Learning Objectives 67
Lesson 1. Isentropic Process 67
Lesson 2. Polytropic Process 70
Assessment 9 72
Summary 73

Module 10: Gas Cycles 74

Introduction 74
Learning Objectives 74
Lesson 1. Cycle Work and Thermal Efficiency 74
Assessment 10 81
Summary 82

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 MODULE 8
PROCESSES OF IDEAL GASES

Introduction

Gases are distinguished from other forms of matter, not only by their power of indefinite
expansion so as to fill any vessel, however large, and by the great effect heat has in dilating
them, but by the uniformity and simplicity of the laws which regulate these changes
(Todayinsci, n.d.).

Learning Outcomes

At the end of this module, students should be able to:

1. Understand the processes of ideal gases.

2. Derive and solve problems using processes of ideal gases;

Lesson 1. Constant Volume Process

An isentropic process is a reversible constant volume process. A constant volume

process may be reversible or irreversible (Sta. Maria, 2008).

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 Figure 8.1 Isometric Process

a. Relation between p and T.

b. Nonflow work

c. The change of internal energy.

d. The heat transferred.

e. the change of enthalpy.

f. the change of entropy.

g. Reversible steady flow constant volume.

(a)

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 (

(b)

(h) Irreversible non-flow constant volume process.

For reversible non-flow,

For irreversible non-flow,

Example

1. Ten cu ft of air at 300 psia and 400 is cooled to 140 at constant volume. What are
(a) the final pressure, (b) the work, (c) the change of internal energy, (d) the transferred
heat, (e) the change of enthalpy, and (f) the change of entropy? (Sta. Maria, 2008).

Solution

Figure 8.2 Constant Volume Diagram

Given:

V = 10 cu ft

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a)

b) W= 0

c)

e)

Lesson 2. Constant Pressure Process

An isobaric process is an internally reversible process of a substance during which the

pressure remains constant (Sta. Maria, 2008).

Figure 8.3 Isobaric Process

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a. Relation between p and T.

b. Non-flow work

c. The change of internal energy.

d. The heat transferred.

e. the change of enthalpy.

f. the change of entropy.

g. Reversible steady flow constant pressure.

(a)

(b)

Example

A perfect gas has a value of R= 319.2 J/kg.K and k=1.26. if 120 kJ are added to 2.27 kg of
this gas at constant pressure when the initial temperature is 32.2 , find
(Sta. Maria, 2008).

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 Figure 8.4. Constant Pressure Diagram

Given:

k = 1.26

m=2.27 kg

R= 319.2 J/kg-K

Q = 120 kW

Solution

a)

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Lesson 3. Constant Temperature Process

As isothermal process is an internally reversible constant temperature process of a

susbstantce (Sta. Maria, 2008).

Figure 8.5 Isothermal Process

a. Relation between p and T.

b. Nonflow work

c. The change of internal energy.

d. The heat transferred.

e. the change of enthalpy.

f. the change of entropy.

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g. steady flow Isothermal

(a)

(b)

Example

Air flows steadily through an engine at constant temperature, 400K. Find the work per
kilogram if the exit pressure is one-third the inlet pressure and the inlet pressure energy
variation is negligible.

Figure 8.6 Constant Temperature Diagram

Given

T – 400 K

R = 287.08 kJ/(kg-K)

Solution

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 Assessment Task 8

1. if 10 kg/min of air are compressed isothermally from and

to , find the work, the change of entrophy and the heat for (a)nonflow
process and b) a steady flow process with and .

Summary

Constant Volume Constant Pressure Constant Temperature

a. Relation between p and T. a. Relation between p and T. a. Relation between p and T.

b. Nonflow work
b. Nonflow work
b. Non-flow work

c. The change of internal energy. c. The change of internal energy.

c. The change of internal energy.
d. The heat transferred. d. The heat transferred.
d. The heat transferred.
e. the change of enthalpy.

e. the change of enthalpy. e. the change of enthalpy.

f. the change of entropy.

f. the change of entropy. f. the change of entropy.

g. Reversible steady flow constant
volume.
g. Reversible steady flow g. steady flow Isothermal
(a)
constant pressure. (a)
(a)
(
(b)
(b)
(b)

(h) Irreversible non-flow constant

volume process.

For reversible non-flow,

For irreversible non-flow,

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 References

Sta. Maria, Hipolito B. (2008). Thermodynamics 1 (1st Edition). National Book

Store. Mandaluyong City.

Todayissci. (n.d). Quotation Categories.

https://todayinsci.com/QuotationsCategories/G_Cat/Gas-Quotations.htm

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 MODULE 9
PROCESSES OF IDEAL GASES

Introduction

“The 2nd law of thermodynamics has the same degree of thrith as the statement that if
you throw a trumblerful of water into the sea, you cannot get the same tumblerful of water
out again” – James Clerk Maxwell, (Izquotes, n.d.).

Learning Outcomes

At the end of this module, students should be able to:

1. Understand the processes of ideal gases.

2. Derive and solve problems using processes of ideal gases;

Lesson 1. Isentropic Process

An isentropic process is a reversible adiabatic process. Adiabatic simply means no heat.

A reversible adiabatic is one of constant entropy (Sta. Maria, 2008).

Figure 9.1 Isentropic Diagram

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1. Relation among p, V, and T.

A) Relation between p and V.

b) Relation between T and V

c) Relation between T and p.

2. Non-flow work.

3. The change of internal energy.

4. The heat transferred.

5. The change of enthalpy.

6. The change of entropy.

7. Steady flow isentropic.

a)

b)

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Example

1. From a state defined by 300 psia 100 cu ft and 240 , helium undergoes and isentropic
process to 0.3, psig. Find a) and , b) and , c) , d) – , e) Q and .
What is the work (f) if the process is non-flow, (g) if the process is steady flow with = 10
Btu? (Sta. Maria, 2008).

Figure 9.2 Isentropic Process

Given:

Solution

a)

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Lesson 2. Polytropic Process

A polytropic process is an internally reversible process during which

(Sta. Maria, 2008).

Where n is any constant.

Figure 9.3 Polytropic Process

1. Relation among p, V, and T.

A) Relation between p and V.

b) Relation between T and V

c) Relation between T and p.

2. Non-flow work.

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3. The change of internal energy.

4. The heat transferred.

5. The change of enthalpy.

6. The change of entropy.

7. Steady flow isentropic.

a)

b)

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 Assessment Task 9

1. a polytropic process of air from 150 psia , 300 , and 1 occurs to in

accordance with Determine (a) and , (b) U, and , (c) and -
and . d) compute the heat from the polytropic specific heat and check by the
equation . (e) Find the non-flow work and (f) the steady flow work for

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 Summary

Isentropic Process Polytropic Process

1. Relation among p, V, and T. 1. Relation among p, V, and T.

A) Relation between p and V. A) Relation between p and V.

b) Relation between T and V

b) Relation between T and V

c) Relation between T and p.

c) Relation between T and p.

2. Non-flow work.

2. Non-flow work.

3. The change of internal energy.

3. The change of internal energy.

4. The heat transferred.

4. The heat transferred.

5. The change of enthalpy.

6. The change of entropy. 5. The change of enthalpy.

7. Steady flow isentropic. 6. The change of entropy.

a)

( 7. Steady flow isentropic.

b) a)

b)

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 References

Izquotes.(n.d). Thermodynamics Quotes. https://izquotes.com/quote/251551

Sta. Maria, Hipolito B. (2008). Thermodynamics 1 (1st Edition). National Book

Store. Mandaluyong City.

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 MODULE 10
GAS CYCLES

Introduction

Ideal cycles are simplified thermodynamic closed cycles to analyze the compression,
combustion, and expansion process in an engine with a focus on extraction of work from
combustion of the fuel–air mixture (Folkson, 2014).

Learning Outcomes

At the end of this module, students should be able to:

1. Understand the principle and specific and latent heat and apply it to gases and vapor;
and
2. Appreciate the process which can be applied to a gas and the corresponding heat and
work energy transfer involved;

Lesson 1. Cycle Work and Thermal Efficiency

Heat engine or thermal engine is closed system (no mass crosses boundaries) that
exchanges only heat and work with its surrounding and that operates in cycles (Sta. Maria,
2008).

Elements of a thermodynamics heat engine with a fluid as the working substance (Sta.
Maria, 2008).

1. A working substance, matter that receives heat, rejects heat, and does work:

2. A source of heat (also called a hot body, a heat reservoir, or just source), from which the
working substance receives heat:

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3. A heat sink (also called a receiver, a cold body, or just sinks), to which the working
substance receives het:

4. An engine, wherein the working substance may do work or have work done it.

A thermodynamics cycle occurs when the working fluid of a system experiences a number of
processes that eventually return the fluid to its initial state.

Cycle Work and Thermal Efficiency

ENGINE

Figure 10.1 Cycle Work Diagram

= Heat Added

Heat Rejected

Net work

Available energy is that part of the heat that was converted into mechanical work.

Unavailable energy is the remainder of the het that had to be rejected into the receiver
(sink) (Sta. Maria, 2008).

The Second Law of Thermodynamics

All energy received as heat by a heat- engine cycle cannot be converted into mechanical
work (Sta. Maria, 2008).

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Work of a cycle

(a)

(Algebraic sum)

( Arithmetic difference)

(b) The net work of a cycle is the algebraic sum of the works done by the individual
processes (Sta. Maria, 2008).

The Carnot Cycle

The carnot cycle is the most efficient cycle conceivable. The are other ideal cycles as
efficient as the Carnot cycle, but none more so , such a perfect cycle forms a standard of
comparison for actual engines and actual cycles and also for other less efficient ideal cycles,
permitting as to judge how much room there might be for improvement (Sta. Maria, 2008).

Figure 10.2. The Carnot Cycle

Operation of the Carnot Engine

A cylinder C contains m mass of a substance. The cylinder head, the only place where
heat may enter or leave the substance (system) is placed in contact with the source of heat

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or hot body which has a constant temperature . Heat flows from the hot body into the
substance in the cylinder isothermally, process 1-2, and the piston moves from 1’ to 2’. Next,
the cylinder is removed from the hot body and the insulator I is placed over the head of the
cylinder, so that no heat may be transferred in or out. As a result, any further process is
adiabatic. The isentropic change 2-3 now occurs and the piston moves from 2’ to 3’. When
the piston reaches the end of the stroke 3’, the insulator I is removed and the cylinder head
is placed in contact with the receiver or sink, which remains at a constant temperature .
Heat then flows from the substance to the sink, and the isothermal compression 3-4 occurs
while the piston moves from 3’ to 4’. Finally, the insulator I is again placed over the head
and the isentropic compression 4-1 returns the substance to its initial condition, as the
piston moves from 4’ to 1’ (Sta. Maria, 2008).

Figure 10.3. Carnot Cycle

Analysis of the Carnot Cycle

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 The thermal efficiency is a defined as the fraction of the heat supplied to a
thermodynamics cycle that is converted into work (Sta. Maria, 2008).

From process 2-3

From process 4-1

But and

Therefore,

Then,

Isothermal expansion ratio =

Isentropic expansion ratio =

Overall expansion ratio =

Compression ratio =

Isothermal compression ratio =

Isentropic Compression ratio,

Overall compression ratio =

The isentropic compression ratio is the compression ratio most commonly used.

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Example:

1. A Carnot power cycle operates on 2 lb of air between the limits of 70 and 500 . The
pressure at the beginning of isothermal; expansion is 400 psia and at the end of isothermal
expansions is 85 psig. Determine (a) the volume at the end of isothermal compression, (b)
during an isothermal process, (c) , (d) , (e) W, (f) e, (g) the ratio of expansion
during isothermal heating and the overall ratio of a expansion, and (h) the mean effective
pressure (Sta. Maria, 2008).

Figure 10.4 Carnot Cycle Diagram

Give:

Point 1:

Point 2:

Point 3:

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Point 4:

(b)

(d)

(g) Isothermal Expansion ratio

Overall expansion ratio

Assessment Task 10

1. A Carnot engine operating between 775 K and 305 K produces 54 kJ of work.

Determine (a) , (b) during heat rejection, and (c) e.

2. Ten of helium at 20 psia and 80 are compressed isentropically 1-2 to 80 psia.

The helium is then expanded polytropically 2-3 with n = 14.35 to the initial temperature.
An Isothermal 3-1 returns the helium to the initials state. Find

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 Summary

Analysis of the Carnot Cycle

References

Folkson, Richard. (2014). Alternative Fuels and Advanced Vehicle Technologies

for Improved Environmental Performance . Science Direct.
https://www.sciencedirect.com/topics/engineering/ideal-cycle

Sta. Maria, Hipolito B. (2008). Thermodynamics 1 (1st Edition). National Book

Store. Mandaluyong City.

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