# ENGSC 2333 Thermodynamics Chapter 3

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27 Οκτ 2013 (πριν από 4 χρόνια και 6 μήνες)

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ENGSC 2333

Thermodynamics

Chapter 3

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To apply the energy balance to a system of interest
requires knowledge of the properties of the system
and how the properties are related. The objective of
Chapter 3 is to introduce property relations relevant
to engineering thermodynamics. We will focus on
the use of the closed system energy balance
introduce in Chapter 2, together with the property
relations considered in this chapter.

Objectives

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Some Concepts and Definitions

State principal

Simple compressible
system

p
-
υ
-
T surface

2
-
phase region

Triple line

Triple point

Saturation state

Vapor dome

Critical point

p
-
υ

diagram

T
-
υ

diagram

Subcooled
(compressed) liquid

Superheated vapor

2
-
phase liquid
-
vapor
mixture

Quality

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3.1 Fixing the State

For simple, compressible systems, the state
principle indicates that the number of
independent intensive properties is
two
.

Intensive properties such as velocity and
elevation that are assigned values relative to
datum
outside

the system are excluded from
present considerations.

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3.2 p
-
υ
-
T Relation

Figure 3.1

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Examples

Virtual pvT diagram

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3.2 Phase Diagram

Figure 3.1

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3.2 T
-
υ

Diagram

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3.2 p
-
υ

Diagram

Figure 3.1

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3.2.3 Quality

For a two
-
phase liquid
-
vapor mixture, the ratio of the
mass of vapor to the total mass of the mixture is call
quality
, represented as
x
.

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ENGSC 2333

Thermodynamics

Chapter 3

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3.3.1 Specific Volume

The specific volume of a two
-
phase liquid
-
vapor mixture
can be determined by using the saturation tables and
the definition of quality.

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3.3.1 Specific Volume

The specific volume of a two
-
phase liquid
-
vapor mixture
can be determined by using the saturation tables and
the definition of quality.

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3.3.2 Specific Internal Energy

The specific internal energy of a two
-
phase liquid
-
vapor
mixture can be determined by using the saturation
tables and the definition of quality.

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3.3.2 Specific Enthalpy

In many thermodynamic
analyses the sum of the
internal energy
U

and the
product of pressure
p

and
volume
V

appears.
Because the sum
U + pV

appears so frequently, we
give this combination a
name,
enthalpy
, and a
distinct symbol,
H
.

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3.3.2 Specific Enthalpy

The specific internal energy of a two
-
phase liquid
-
vapor
mixture can be determined by using the saturation
tables and the definition of quality.

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Examples

For water at the following conditions, determine
the phase or phases present:

1.
T = 40
º
C, P = 0.09593 bar

2.
T = 250
º
C, P = 39.73 bar,
υ

= 0.04 m
3
/kg

3.
T = 250
º
C, P = 39.73 bar,
υ

= 0.0012512 m
3
/kg

4.
T = 90
º
F,
υ

= 500 ft
3
/lb
m

5.
P = 50 psi,
υ

= 0.01727 ft
3
/lb
m

6.
P = 50 psi, m = 10 kg

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3.3.5 Evaluating specific heats

The intensive properties c
v

and c
p

are
defined for pure, simple
compressible substances as partial
derivatives of the functions u(T,v)
and h(T,p) respectively.

We also use the specific heat ratio, k.

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3.3.5 Evaluating specific heats

Figure 3.9 c
p

of water vapor

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3.3.6
Incompressible substance model

Approximations for liquids using saturated liquid data:

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3.3.6 Incompressible substance model

For a substance modeled as incompressible, the specific
heats c
v

and c
p

are equal.

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3.3.6 Incompressible substance model

Assuming the specific heats are constant (not a function
of temperature)…

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3.4 Generalized compressibility chart

The ideal gas law:

Where:

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3.4 Generalized compressibility chart

For ideal gases:

Where:

Always use absolute pressures and
temperatures!!!

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3.4 Generalized compressibility chart

Universal gas constant:

Compressibility factor:

Figure 3.10

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3.4 Generalized compressibility chart

For compressible gases:

Where:

Always use absolute pressures and
temperatures!!!

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3.4 Generalized compressibility chart

For compressible gases:

Where:

Always use absolute pressures and
temperatures!!!

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3.4 Generalized compressibility chart

Figure 3.11

Z values from Figures A
-
1,
A
-
2, and A
-
3 in appendices.

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The principle of corresponding states:

Reduced pressure:

Reduced temperature:

3.4 Generalized compressibility chart

Figure 3.2

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The principle of corresponding states:

3.4 Generalized compressibility chart

Figure 3.12

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3.5 Ideal gas model properties

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Examples

For water at 374.15
º
C and 219.9 bar (gage),
determine:

1.
P
R

2.
T
R

3.
Z

Assume P
atm
=1 bar

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ENGSC 2333

Thermodynamics

Chapter 3

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3.4 Generalized compressibility chart

Compressibility factor:

Reduced pressured:

Reduced temperature:

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The principle of corresponding states:

3.4 Generalized compressibility chart

Figure 3.12

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3.4 Generalized compressibility chart

Figure 3.3

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3.5 Ideal gas model properties

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3.5 Ideal gas model properties

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c
p

in Table A
-
19

Note: c
v

not given

For monatomic
gases, c
p
=(5/2)R

3.5 Ideal gas model properties

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3.6 U and H of ideal gases

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Values of the constants are listed in Table A
-
21.

3.6 Specific heat functions

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Using ideal gas tables (A
-
22 and A
-
23)…

Evaluate the change in specific enthalpy for air from a state where
T
1
=400 K to a state where T
2
=900 K.

3.7 Specific heats… simplified

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Assuming constant specific heats (A
-
20)…

Evaluate the change in specific enthalpy for air from a state where
T
1
=400 K to a state where T
2
=900 K.

3.7 Specific heats… simplified

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For a polytropic process of a closed system…

3.8 Polytropic processes of an Ideal Gas

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For a polytropic process of a closed system…

Isobaric

Isothermal

Also, when specific heats are constant, the value of the exponent
n

corresponding to an adiabatic polytropic process of an ideal gas is
the specific heat ratio,
k
.

3.8 Polytropic processes of an Ideal Gas

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3.8 Polytropic processes of an Ideal Gas

Valid for
any

gas.

Remember from Chapter 2…

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3.8 Polytropic processes of an Ideal Gas

Valid for
ideal gases.

Using pV=mRT…