INTRODUCTION
Thermodynamics can be defined as the science of energy. Although everybody has a feeling of what energy
is, it is difficult to give a precise definition for it. Energy can be viewed as the ability to cause changes.
The name thermodynamics stems from the Greek words therme (heat) and dynamis (power), which is most
descriptive of the early efforts to convert heat into power.
Thermodynamics is the science dealing with the relations between the properties of a system and the
quantities that are used to define the state of a system. Hence a knowledge of is properties is required.
A thermodynamic property must be a characteristic that can be measured, and must have a unique numerical
value when the fluid is in any state. The value of a property must be independent of the process through
which the fluid must have passed in reaching that state. It follows that when a system changes state, the
changes in properties are only dependent on the initial and final states of the system. Example of some of
the properties are pressure, volume and temperature.
TEMPERATURE
Temperature can be simply defined as the degree of hotness or coldness of a body. Based on our
physiological sensations, we express the level of temperature qualitatively with words like freezing cold, cold,
warm, hot, and red-hot. However, we cannot assign numerical values to temperatures based on our
sensations alone. It is not easy to give an exact definition for it.
In other words, Temperature is defined as the average kinetic energy of the individual molecules that
comprise the component of a system.
Temperature and The Zeroth Law of Thermodynamics
It is a common experience that a cup of hot coffee left on the table eventually
cools off and a cold drink eventually warms up. That is, when a body is
brought into contact with another body that is at a different temperature, heat
is transferred from the body at higher temperature to the one at lower
temperature until both bodies attain the same temperature. At that point, the
heat transfer stops, and the two bodies are said to have reached thermal
equilibrium. The equality of temperature is the only requirement for thermal
equilibrium.
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(Fig. 1.1) Two bodies reaching thermal
equilibrium after being brought into
contact in an isolated enclosure.
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When two bodies are said to have same temperature, that means there is no change in any of their
observable characteristics when brought in contact with one another
The zeroth law of thermodynamics states that if two bodies are in thermal equilibrium with a third body,
they are also in thermal equilibrium with each other i.e. if body A is equal in temperature to body B and body
A is also equal in temperature to a third body C, body B must be in equal in temperature to body C.
The zeroth law of thermodynamics provides the basis for the measurement of temperature. By replacing the
third body with a thermometer, the zeroth law can be restated as two bodies are in thermal equilibrium if both
have the same temperature reading even if they are not in contact.
TEMPERATURE MEASUREMENT
Temperature is the most widely monitored parameter in the field of science and industry. As such,
temperature measurement is very important in all spheres of life.
A thermometer is an instrument used to measure the temperature of a body. It can determine the temperature
of a body or even of air or atmosphere. The instrument used to measure temperature can be divided into
separate classes according to the physical principles on which they operate. The main principles used are:
•
Thermal expansion (Liquid-in-glass thermometer, bimetallic & pressure strips)
•
Thermoelectric effect (thermocouple)
•
Resistance change (Resistance thermometer, thermistors)
•
Sensitivity of semiconductor device
•
Radiative heat emission (optical pyrometers)
•
Thermography
•
Change of state of material
The physical properties of the materials which change uniformly with temperature and used for measuring
the temperature are called thermometric properties and the materials used for making thermometers are
called thermometric substances.
Common thermometers are generally made using some suitable liquid as thermometric material and the
names of the corresponding thermometric properties employed are given below:
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Thermometer
Thermometric property
Constant volumes gas
Pressure (p)
Constant pressure gas
Volume (V)
Alcohol or mercury-in-glass
Length (L)
Electric resistance
Resistance (R)
Thermocouple
Electromotive force (E)
Radiation (pyrometer)
Intensity of radiation (I or J)
Table 1.1
Consequently, there are five good thermometric substances which are.
•
Mercury and alcohol,
•
All gases,
•
Platinum,
•
Thermocouples,
•
Radiant energy.
Common thermometer used may be classified in two broad categories:
1. Non-electrical methods:
i.
By using change in volume of a liquid when its temperature is changed.
ii.
By using change in pressure of a gas when its temperature is changed.
iii.
By using changes in the vapour pressure when the temperature is changed.
2. Electrical method:
i.
By thermocouples.
ii.
By change in resistance of material with change in temperature.
iii.
By comparing the colours of filament and the object whose temperature is to be found out.
iv.
By ascertaining the energy received by radiation.
The thermometers may also be classified as follows:
1. Expansion thermometers
(i) Liquid-in-glass thermometers (ii) Bimetallic thermometers.
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2. Pressure thermometers
(i) Vapour pressure thermometers (ii) Liquid-filled thermometers (iii) Gas-filled thermometers.
3. Thermocouple thermometer
4. Resistance thermometers
5. Radiation pyrometers
6. Optical pyrometers.
1. Expansion Thermometers:
The expansion thermometers make use of the differential expansion of two different substances. Thus, in
liquid-in-glass thermometers, it is the difference in expansion of liquid and the containing glass. And in
bimetallic thermometers, the indication is due to the difference in expansion of the two solids. These
thermometers are discussed below:
(i) Liquid-in-glass thermometer: This is a very familiar type of thermometer. The mercury or other liquid fills
the glass bulb and extends into the bore of the glass stem. Mercury is the most suitable liquid and is used
from – 38.9°C (melting point) to about 600°C. The thermometers employed in the laboratory have the scale
engraved directly on the glass stem.
A usual type of mercury-in-glass thermometer is shown in Fig. 1.2. An expansion bulb
is usually provided at the top of the stem to allow room for expansion of mercury, in
case the thermometer is subjected to temperature above its range. The upper limit for
mercury-in-glass thermometers is about 600°C. As the upper limit is far above the
boiling point of mercury, some inert gas i.e., nitrogen is introduced above the mercury
to prevent boiling.
Bimetallic strip thermometers: In a bimetallic thermometer differential expansion of
bimetallic strips is used to indicate the temperature. It has the advantage over the liquidin-glass thermometer, that it is less fragile and is easier to read. In this type of thermometer
two flat strips of different metals are placed side by side and are welded together. Many
different metals can be used for this purpose. Generally, one is a low expanding metal
and the other is high expanding metal. The bimetal strip is coiled in the form of a spiral
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Fig. 1.2: Mercury –in- glass
Thermometer
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or helix. Due to rise in temperature, the curvature of the strip changes. The differential expansion of a strip
causes the pointer to move on the dial of the thermometer.
Bimetallic strip thermometers are used in refrigerators for temperature regulation. They are also used in
thermometer. The thermometer records a graph of temperature. Instead of a pointer, a pen is attached to the
bimetallic strip, which records the temperature on a moving chart. The chart of the temperature is called a
thermogram.
2. Pressure thermometers are discussed below:
(i)
Vapour pressure thermometer:
A schematic diagram of a vapour pressure thermometer is shown in Fig. 1.3. When the bulb containing the
fluid is installed in the region whose temperature is required, some of the fluid vapourizes, and increases the
vapour pressure. This change of pressure is indicated on the Bourdon tube. The relation between
temperature and vapour pressure of a volatile liquid is of the exponential form. Therefore, the scale of a
vapour pressure thermometer will not be linear.
Fig. 1.3 Vapour pressure thermometer
(ii)
Liquid-filled thermometer:
A liquid-filled thermometer is shown in Fig. 1.4. In this case, the expansion of the liquid causes the pointer to
move in the dial. Therefore, liquids having high co-efficient of expansion should be used. In practice many
liquids e.g., mercury, alcohol, toluene and glycerin have been successfully used. The operating pressure
varies from about 3 to100 bar. These types of thermometers could be used for a temperature up to 650°C in
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which mercury could be used as the liquid. In actual design, the internal diameter of the capillary tube and
Bourdon tube is, made much smaller than that of the bulb. This is because the capillary tube is subjected to
a temperature which is quite different from that of the bulb. Therefore, to minimise the effect of variation in
temperature to which the capillary tube is subjected, the volume of the bulb is made as large as possible as
compared with the volume of the capillary. However, large volume of bulb tends to increase time lag,
therefore, a compensating device is usually built into the recording or indicating mechanism, which
compensates the variations in temperature of the capillary and Bourdon tubes.
(iii)
Gas-filled thermometers:
The temperature range for gas thermometer is practically the same as that of liquid filled thermometer. The
gases used in the gas thermometers are nitrogen and helium. Both these gases are chemically inert, have
good values for their co-efficient of expansion and have low specific heats. The construction of this type of
thermometer is more or less the same as mercury-thermometer in which Bourdon spring is used. The errors
are also compensated likewise. The only difference in this case is that bulb is made much larger than used
in liquid-filled thermometers. For good performance the volume of the bulb should be made at least 8 times
than that of the rest of the system. These thermometers are generally used for pressures below 35 bar.
3. Thermocouple Thermometers:
For higher range of temperature i.e., above 650°C, filled thermometers are unsuitable. For higher range of
temperature, thermocouples and pyrometers are used. Copper leads
Fig: 1.4: Thermocouple
In its simplest form a thermocouple consists of two dissimilar metals or alloys which develop e.m.f. when the
reference and measuring junctions are at different temperatures. The reference junction or cold junction is
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usually maintained at some constant temperature, such as 0°C. Fig. 1.4, shows a simple circuit of a
thermocouple and the temperature measuring device. In many industrial installations the instruments are
equipped with automatic compensating devices for temperature changes of the reference junction, thus
eliminating the necessity of maintaining this junction at constant temperature.
Table 1.2 gives the composition, useful temperatures range and temperature versus e.m.f. relationship for
some commercial thermocouples.
Temp. (oC)
S/No.
Thermocouple
Composition
Useful
range
1. Platinum vs
Platinum-rhodium
Pure Platinum
400 to
vs Pt + 10 or
1450
Max.
1700
13% Rh
2. Chromel vs
alumel
3. Iron vs
Constantan
90% Ni
+10%Cr vs
-200 to
1450
1200
Constantan
(oC)
Millivolt
0
0.0
Used for high
4.212
temp.
1000
9.569
measurements
1500
15.498
-200
-5.75
0.0
300
12.21
(Al + Sn) Mn
600
24.90
900
37.36
1200
48.85
-200 to
40-60% Cu +
750
1000
Pure copper
vs Cu-Ni
-200 to
600
350
constantan
High
resistance to
95% Ni + 5%
Pure Iron vs
Remarks
500
0
55-40% Ni
4. Copper vs
Thermoelectric power
oxidation
-200
-8.27
0
0.0
300
16.59
600
33.27
900
52.29
-200
-5.539 Not suitable in
--
0
0.0 air due to
200
9.285 excessive
400
20.865 oxidation
Table 1.2
4. Resistance thermometers:
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The fact that the electrical resistance of the metals increases with temperature is made use of in resistance
thermometers which are purely electrical in nature. A resistance thermometer is used for precision
measurements below 150°C. A simple resistance thermometer consists of a resistance element or bulb,
electrical loads and a resistance measuring or recording instrument. The resistance element (temperature
sensitive element) is usually supplied by the manufacturers with its protecting tube and is ready for electrical
connections. The resistance of the metal used as resistance element should be reproducible at any given
temperature. The resistance is reproducible if the composition or physical properties of the metal do not
change with temperature. For this purpose, platinum is preferred. A platinum resistance thermometer can
measure temperatures to within ± 0.01°C. However, because of high cost of platinum, nickel and copper are
used as resistance elements for industrial purposes for low temperatures. The fine resistance wire is wound
in a spiral form on a mica frame. The delicate coil is then enclosed in a porcelain or quartz tube. The change
of resistance of this unit can be measured by instruments such as Wheatstone bridge, potentiometer or
galvanometer.
The resistance thermometers possess the following advantages over other devices:
i.
A resistance thermometer is very accurate for low ranges below 150°C.
ii.
It requires no reference junction like thermocouples and as such is more effective at room
temperature.
iii.
The distance between the resistance element and the recording element can be made much larger
than is possible with pressure thermometers.
iv.
It resists corrosion and is physically stable.
Disadvantages:
i.
The resistance thermometers cost more.
ii.
They suffer from time lag.
5. Radiation pyrometers:
A device which measures the total intensity of radiation emitted from a body is called radiation pyrometer.
The elements of a total radiation pyrometer are illustrated in Fig. 1.5. It collects the radiation from an object
(hot body) whose temperature is required. A mirror is used to focus this radiation on a thermocouple. This
energy which is concentrated on the thermocouple raises its temperature, and in turn generates an e.m.f.
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This e.m.f. is then measured either by the galvanometer or potentiometer method. Thus, rise of temperature
is a function of the amount of radiation emitted from the object.
Fig. 1.5. A schematic diagram of radiation pyrometer
Advantages of the pyrometers
1. The temperatures of moving objects can be measured.
2. A higher temperature measurement is possible than that possible by thermocouples etc.
3. The average temperatures of the extended surface can be measured.
4. The temperature of the objects which are not easily accessible can be measured.
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TEMPERATURE SCALES
Temperature scales enable us to use a common basis for temperature measurements, and several have
been introduced throughout history. All temperature scales are based on some easily reproducible states
such as the freezing and boiling points of water, which are also called the ice point and the steam point,
respectively.
The temperature scales used in the SI and in the English system today are the Celsius scale (formerly called
the centigrade scale; in 1948 it was renamed after the Swedish astronomer Anders Celsius, 1702–1744, who
devised it) and the Fahrenheit scale (named after the German instrument maker Daniel Gabriel Fahrenheit,
1686–1736), respectively. The Celsius scale is based on the boiling/freezing point of water (at sea level) i.e.
100 & 0°C respectively. There is no upper limit in this scale, lower limit is equal to -273°C. The corresponding
values on the Fahrenheit scale are 32 and 212°F. These are often referred to as two-point scales since
temperature values are assigned at two different points.
In thermodynamics, it is very desirable to have a temperature scale that is independent of the properties of
any substance or substances. Such a temperature scale is called a thermodynamic temperature scale,
which is developed later in conjunction with the second law of thermodynamics. The thermodynamic
temperature scale in the SI is the Kelvin scale, named after Lord Kelvin
(1824–1907). The temperature unit on this scale is the kelvin, which
is designated by K (not °K; the degree symbol was officially dropped from
kelvin in 1967). The lowest temperature on the Kelvin scale is absolute zero,
or 0 K. Then it follows that only one nonzero reference point needs to be
assigned to establish the slope of this linear scale. Using nonconventional
refrigeration techniques, scientists have approached absolute zero kelvin
(they achieved 0.000000002 K in 1989). Zero level for any scale is arbitrary.
The thermodynamic temperature scale in the English system is the Rankine
scale, named after William Rankine (1820–1872). The temperature unit on
this scale is the rankine, which is designated by R. The reference temperature
chosen in the original Kelvin scale was 273.15 K (or 0°C), which is the
temperature at which water freezes (or ice melts) and water exists as a solid–
liquid mixture in equilibrium under standard atmospheric pressure (the ice
point).
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(Fig. 1.6) Comparison btw temperature
scales
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The Kelvin scale is related to the Celsius scale by:
T(K) = T(°C) + 273.15
The Rankine scale is related to the Fahrenheit scale by:
T(R) = T(°F) + 459.67
The temperature scales in the two unit systems are related by:
T(R) = 1.8T (K)
T(°F) = 1.8T (°C) + 32
Based on the available method of measurement, the whole temperature scale may be divided into four ranges.
The equations for interpolation for each range are as follows:
1. From – 259.34°C (triple point of hydrogen) to 0°C:
A platinum resistance thermometer of a standard design is used and a polynomial of the following form is fitted
between the resistance of the wire Rt and temperature t
Rt = R0 (1 + At + Bt2 + Ct3)
..........................
(1-1)
Where R0 = resistance at the ice point.
2. From 0°C to 630.74°C (Antimony point):
i.
It is also based on platinum resistance thermometer.
ii.
The diameter of the platinum wire must lie between 0.05 and 0.2 mm.
3. From 630.74°C to 1064.43°C (Gold point):
i.
It is based on standard platinum versus platinum-rhodium thermocouple.
ii.
Following equation between e.m.f. “E” and temperature “t” is employed:
E = a + bt + ct2
..........................
(1-2)
4. Above 1064.43°C:
It is based on the intensity of radiation JT at temperature T emitted by a black body at a wavelength λ in the visible
spectrum and by comparing this to the intensity of radiation JAu at the same wavelength emitted by a black body
at the gold point.
The temperature is calculated from Planck’s equation for black body radiation
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𝐶
𝑒𝑥𝑝 ( 2 ) − 1
𝐽𝑇
𝜆𝑇𝐴𝑈
=
……………………
𝐶2
𝐽𝐴𝑈
𝑒𝑥𝑝 ( ) − 1
𝜆𝑇
1−3
Where C2 = 0.01438 in °C, and λ = wavelength in metres.
Following points are worth noting for gas thermometers:
a. The gas thermometers are never used for the measurement of temperatures. However, they are ideal when
used for calibration for establishing the ideal gas temperature scale, and for establishing a standard because
of precision, reproducible results, and their reading being independent of the thermometric substance used.
b. The gas thermometers can be used only for temperatures up to which gases do not liquify.
c. Celsius and Fahrenheit scales are the two commonly used scales for the measurement of temperature.
Symbols C and F are respectively used to denote the readings on these two scales. Until 1954 the
temperature scales were based on two fixed points: (i) the steam point (boiling point of water at standard
atmospheric pressure), and (ii) the ice point (freezing point of water).
The fixed points for these temperature scales are:
Temperature
Celsius scale
Fahrenheit scale
Steam point
100
212
Ice point
0
32
Interval
100
180
Table 1.4
d. The relation between a particular value C on Celsius scale and F on Fahrenheit scale is found to be
as mentioned below:
𝐶
𝐹 − 32
=
100
180
𝑜𝑟
𝐶 𝐹 − 32
=
…………………
5
9
1−4
Example 1.1
During a heating process, the temperature of a system rises by 10°C. Express this rise in temperature in K,
°F, and R.
Solution:
The temperature rise of a system is to be expressed in different units.
This problem deals with temperature changes, which are identical in Kelvin and Celsius scales. Then,
∆𝑇 (𝐾) = ∆𝑇 (℃) = 10𝐾
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The temperature changes in Fahrenheit and Rankine scales are also identical and are related to the changes
in Celsius and Kelvin scales.
∆𝑇 (𝑅) = 1.8∆𝑇 (𝐾) = 1.8 (10) = 18𝑅
And;
∆𝑇 (℉) = ∆𝑇 (𝑅) = 18℉
Note that the units °C and K are interchangeable when dealing with temperature differences.
Example 1.2
Consider a system whose temperature is 18°C. Express this temperature in R, K, and °F.
IDEAL GAS
Property tables provide very accurate information about the properties, but they are bulky and vulnerable to
typographical errors. A more practical and desirable approach would be to have some simple relations among the
properties that are sufficiently general and accurate. Any equation that relates the pressure, temperature, and specific
volume of a substance is called an equation of state. Property relations that involve other properties of a substance
at equilibrium states are also referred to as equations of state. There are several equations of state, some simple and
others very complex. The simplest and best-known equation of state for substances in the gas phase is the ideal-gas
equation of state. This equation predicts the P-v-T behavior of a gas quite accurately within some properly selected
region.
Gas and vapor are often used as synonymous words. The vapor phase of a substance is customarily called a gas
when it is above the critical temperature. Vapor usually implies a gas that is not far from a state of condensation.
In 1662, Robert Boyle, an Englishman, observed during his experiments with a vacuum chamber that the pressure of
gases is inversely proportional to their volume.
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If P is the absolute pressure of the gas and v is the volume occupied by the gas, then
𝑉𝛼
1
𝑜𝑟
𝑃
𝑃𝑣 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡, 𝑠𝑜 𝑙𝑜𝑛𝑔 𝑎𝑠 𝑡𝑒𝑚𝑝. 𝑖𝑠 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡.
Fig. .1.7 shows the graphical representation of Boyle’s law. The curves are rectangular hyperbolas asymptotic to the
p-v axis. Each curve corresponds to a different temperature. For any two points on the curve,
𝑃1 𝑣2
=
𝑃2 𝑣1
Fig. .1.7
In 1802, J. Charles and J. Gay-Lussac, Frenchmen, experimentally determined that at low pressures the volume of a
gas is proportional to its temperature. In other words,
𝑣 𝛼 𝑇 𝑜𝑟
𝑣
= 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡, 𝑎𝑠 𝑙𝑜𝑛𝑔 𝑎𝑠 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑖𝑠 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡.
𝑇
If a gas changes its volume from V1 to V2 and absolute temperature from T1 to T2 without any change of pressure, then
𝑣1 𝑣2
=
𝑇1 𝑇2
An ‘ideal gas’ is defined as a gas having no forces of intermolecular attraction. The gases which follow the gas laws at
all ranges of pressures and temperatures are considered as “ideal gases”. However, ‘real gases’ follow these laws at
low pressures or high temperatures or both. This is because the forces of attraction between molecules tend to be very
small at reduced pressures and elevated temperatures. An ideal gas obeys the law:
𝑇
𝑃 = 𝑅 ( ) 𝑜𝑟 𝑃𝑣 = 𝑅𝑇
𝑣
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Equation 2–1 is called the ideal-gas equation of state, or simply the ideal-gas relation, where the constant of
proportionality R is called the gas constant.
In this equation, P is the absolute pressure, T is the absolute temperature, and v is the specific volume. The specific
heat capacities are not constant but are functions of temperature.
The gas constant R is different for each gas and is determined from:
𝑅=
𝑅𝑜
𝑘𝐽
𝑘𝑃𝑎. 𝑚3
(
𝑜𝑟
)
𝑀 𝑘𝑔. 𝐾
𝑘𝑔. 𝐾
………………
Substance
2−2
R, kJ/kg.K
Air
0.2870
Helium
2.0769
Argon
0.2081
Nitrogen
0.2968
Table 1-1
where R0 is the universal gas constant and M is the molar mass also called molecular weight) of the gas. The constant
R0 is the same for all substances, and its value is R0 = 8.31447 kJ/kg. K or kPa.m3/kg. K
The mass of a system is equal to the product of its molar mass M and the mole number N:
𝑚 = 𝑀𝑁
(𝑘𝑔) … … … … … …
2−3
The ideal-gas equation of state can be written in several different forms: for m kg, occupying v m3:
𝑃𝑣 = 𝑚𝑅𝑇 … … … … … … … …
2−4
By writing Eq. 2–4 twice for a fixed mass and simplifying, the properties of an ideal gas at two different states are
related to each other by
𝑃1 𝑣1 𝑃2 𝑣2
=
………………
𝑇1
𝑇2
2−5
Example 1.3
Determine the mass of the air in a room whose dimensions are 4 m x 5 m x 6 m at 100 kPa and 25°C.
Solution:
Air at specified conditions can be treated as an ideal gas. From Table 1–1, the gas constant of air is R = 0.287 kPa ·
m3/kg · K, and the absolute temperature is
T = 25°C + 273 = 298 K.
The volume of the room is
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V = (4m) x (5m) x (6m) = 120m3
The mass of air in the room is determined from the ideal-gas relation to be
𝑚=
𝑃𝑣
100 × 120
=
= 140.3𝑘𝑔
𝑅𝑇
0.287 × 298
For engineering calculations, the equation of state for perfect gases can be used for real gases so long as the pressures
are well below their critical pressure and the temperatures are above the critical temperature because at low pressures
and high temperatures, the density of a gas decreases, and the gas behaves as an ideal gas under these conditions.
Example 1.4.
The volume of a high altitude chamber is 40 m3. It is put into operation by reducing pressure from 1 bar to 0.4 bar and
temperature from 25°C to 5°C. How many kg of air must be removed from the chamber during the process? Express
this mass as a volume measured at 1 bar and 25°C. Take R = 287 J/kg K for air.
Solution.
V1 = 40 m3, V2 = 40 m3
P1 = 1 bar, P2 = 0.4 bar
T1 = 25 + 273 = 298 K T2 = 5 + 273 = 278 K
kg of air to be removed:
𝑚=
𝑣=
𝑃2 𝑣2
0.4 × 40
=
=
𝑅𝑇2
0.287 × 278
𝑚𝑅𝑇1
× 0.287 × 298
=
=
𝑃1
1
The P-v-T Surface of an Ideal Gas
The state of a simple compressible substance is fixed by any two independent, intensive properties. Once the two
appropriate properties are fixed, all the other properties become dependent properties. Remembering that any equation
with two independent variables in the form z = z(x, y) represents a surface in space, we can represent the P-v-T
behavior of a substance as a surface in space.
The equation of state of an ideal gas is a relationship between the variables pressure (p), volume (V) and temperature
perpendiculars axes, we get a surface which represents the equation of state (pv = RT). Such a surface is called p-vT surface. These surfaces represent the fundamental properties of a substance and provide a tool to study the
thermodynamic properties and processes of that substance. Fig. 1.9 shows a portion of a p-v-T surface for an ideal
gas. Each point on this surface represents an equilibrium state and a line on the surface represents a process. The
Fig1.9 also shows the constant pressure, constant volume and constant temperature lines.
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Fig. 1.9
Example 1.2.
A steel flask of 0.04 m3 capacity is to be used to store nitrogen at 120 bar, 20°C. The flask is to be protected
against excessive pressure by a fusible plug which will melt and allow the gas to escape if the temperature
rises too high.
(i) How many kg of nitrogen will the flask hold at the designed conditions?
(ii) At what temperature must the fusible plug melt in order to limit the pressure of a full flask to a maximum
of 150 bar?
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