Thermodynamic properties

Thermodynamic Properties
&
Measurement
Dr. Rohit Singh Lather

Important fundamental base SI units
• Mass: Kilogram (kg), Pound (lbm)
– Kilogram (kg): is a mass equal to the mass of the international prototype of the kilogram (a
platinum-iridium bar stored in Paris), roughly equal to the mass of one liter of water at
standard temperature and pressure
• Length: Meter (m), Foot (ft)
– Meter (m): the length of the path traveled by light in vacuum during a time interval of
1/299792458 of a second
• Time: seconds (s)
– Second: (s), the duration of 9192631770 periods of the radiation corresponding to the
transition between the two hyperfine levels of the ground state of the cesium 133 atom
• Temperature: an equilibrium property which roughly measures how hot or cold an object is
- Note our senses are poor judges of temperature
- Our bodies actually have more sensitivity to heat fluxes instead of temperature;
heat leaves our body more rapidly when in contact with high density objects like
snow relative to that of low density objects like air
Introduction
Source: Joseph M. Powers, “Lecture notes on thermodynamics", University of Notre Dame, Notre Dame, Indiana, USA

- Kelvin: (K) the fraction 1/273.16 of the thermodynamic temperature of the triple point of water
– Rankine: (◦R)
• Energy: roughly speaking, the ability to do work, found from the product of force and distance
– Joule: (J), 1 J = 1 (N m)
– Foot-pound force: (ft lbf)
• Specific Volume: the volume per unit mass, known as v = V/m
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• Density: the mass per unit volume, the inverse of specific volume ρ = m/V

Pressure
1 Pa = 1 N/m2
1 bar = 1 x 105 Pa = 0.1 MPa
1 atm = 101325 Pa
1 torr = 133.3 Pa
Static and Dynamic Pressure
The unit of pressure are Pa, psi, atm., bar, torr
force in newton or lb
area in m2 or in2
Dynamic Pressure
Pressure exerted by a fluid or gas when it impacts on a
surface or an object due to its motion or flow
Static Pressure
Pressure of fluid or gases that
are stationary or not in motion
• Pressure as the normal component of force per unit area (exerts on solids, gas and liquid)
P =
)
*
Note that stress is not a true pressure since it is not scalar
Pressure is related to momentum, while temperature is related to kinetic energy

• In most thermodynamic investigations we are concerned with absolute pressure
• In thermodynamics, we are almost always concerned with the absolute pressure as opposed to the
gauge pressure
• Most pressure and vacuum gauges read the difference between the absolute pressure and the
atmospheric pressure existing at the gauge. This is referred to as gauge pressure
The gauge and absolute pressures are related via the formula
Pgauge = Pabsolute − Patm.
We nearly always interpret P as an absolute pressure, so we could also say
Pgauge = P − Patm.
– Pascal: (Pa), 1 Pa = 1 N/m2;
1 bar = 105 Pa, 1 atm = 1.01325 × 105 Pa = 101.325 kPa = 0.101325 MPa
– (psia): 1 psia = 1 lbf/in.2
1 atm = 14.696 psia.
The a denotes the “absolute” pressure as opposed to the “gauge” pressure.
The units psig refer to a gauge pressure

• Pressure is a property of fluids, which, by definition cannot support a shear
• Stress comes in three forms:
• Tensile/compressive stresses are related to forces normal to a surface
• Shear stresses are in the plane of the surface
• The bulk modulus is related to hydrostatic forces (pressure)
• Except for the fact that the bulk modulus is measured by applying hydrostatic pressure, stress
relates to properties of solids

Absolute zero reference
Pressure
Absolute Pressure
Gauge Pressure
Local atmospheric
Pressure reference
Gauge Pressure
Suction/Vacuum
Gauge Pressure is relative pressureAbsolute Pressure is Real Pressure
(pg > 0 or pg < 0; while pabs > 0 always) ∴ pabs = pg + patm > 0
Gauge Pressure
Pressure measured w.r.t
atmospheric pressure
(unit = psig)
Absolute Pressure
Pressure measured w.r.t a
vacuum
(unit = psia)
Atmospheric Pressure
Pressure on the earth’s surface due to the
weight of gases in the earth’s atmosphere

Pressure Measuring Instrument
• The techniques for pressure measurement is depending on pressure level. (moderate, very high,
very low)
Very high pressure level is higher than 1000 bar
Very low pressure level is below than 0.001 bar
Low Pressure Measurement
- McLeod gauge
- Pirani gauge
- Ionization gauge
High Pressure Measurement
- Electrical Resistance pressure gauge
Moderate Pressure Measurement
- Manometer
- Elastic elements (diaphragm, bellows, capsules, bourdon tubes, spiral, helix)

Manometer
• Manometer: a pressure measuring instrument, usually limited to measuring pressures near to
atmospheric
• Pressures below atmospheric and slightly above atmospheric, and pressure differences (for
example, across an orifice in a pipe), are frequently measured with a manometer, which contains
water, mercury, alcohol, oil, or other fluids.
• The term manometer is often used to refer specifically to liquid column hydrostatic instruments
• Manometer is the simplest device for measuring static pressure
ΔP = m.g.Δh
Pressure line
connected
Fluid
water/ mercury or any
other suitable fluid in
the manometer tube
Column forced down
Fluid rises
Measure the difference
in height of the fluid in
the two columns
Pressure of the inlet can be
expressed in inches of fluid

Fluid at P,
mg
PatmA
PA
PATM
A
g
y
Newton's Second Law of motion m
+,
-
+&, = P.A − Patm .A − m.g
For static cases, the acceleration
+,
-
+&, = 0
Thus, we require a force balance, i.e. mechanical
equilibrium, which is achieved when
0 = P.A − Patm.A − m.g
P.A = Patm.A + m.g
So, Thus, P.A = PatmA + ρ.A.H.g
P = Patm + ρ.g.H
∆P = P − Patm = Pgauge = ρ.g.H
m.g = ρ.V.g
V is the volume of the fluid
V = A.H
H
m.g = ρ.A.H.g
ρ

Types of Manometer
U-tube Manometer Well-type Manometer Incline-tube Manometer
Photo Source: www.cnx.org

• Absolute pressure is zero referenced against a “perfect vacuum” (it-the value-is equal to gauge
pressure plus atmospheric pressure)
• Gauge pressure is zero referenced against ambient air pressure; it-the value-is equal to absolute
pressure minus atmospheric pressure. Negative signs are usually omitted; often expressed as
“inches of vacuum” or some such
• Differential pressure is the difference in pressure between two points

Mercury Barometer
Mercury Barometer measures atmospheric pressure
Pressure due to weight of mercury
equals atmospheric pressure
The atmosphere is able to force
mercury in the tube of a height because
the pressure above the mercury is zero

Hydrostatic Pressure
• Hydrostatic pressure is the pressure in a liquid
• The pressure increases as the depth in a liquid increases, due to its weight
• In term of equation, P = ρgh
ρ = density in kg/m3
g = acceleration due to gravity (9.8m/s2)
h = depth in liquid in m
P = pressure in Pa
Hydrostatic gauges (such as the mercury column manometer) compare pressure to the hydrostatic
force per unit area at the base of a column of fluid
Hydrostatic gauge measurements are independent of the type of gas being measured, and can be
designed to have a very linear calibration. They have poor dynamic response

Piston Types Gauge
• Piston-type gauges counterbalance the pressure of a fluid with a solid weight or a spring
• For example dead-weight testers used for calibration and Tire-pressure gauges

Mechanical Gauges – Bourdon type, Bellows type
• Key concept: pressure difference across different areas of inner and outer surfaces causes
crescent to flex

Heat
• For quantitative purposes we utilize the change of volume which takes place in all bodies when
heated under constant pressure, for this admits of exact measurement
• Heating produces in most substances an increase of volume, and thus we can tell whether a body
gets hotter or colder, not merely by the sense of touch, but also by a purely mechanical
observation affording a much greater degree of accuracy
• The conception of heat arises from that particular sensation of warmth or coldness which is
immediately experienced on touching a body
Direct sensation, however,
- gives no quantitative scientific measure of a body's state with regard to heat
- It yields only qualitative results, which vary according to external circumstances
Source: Treatise on Thermodynamics , DR. Max Plank, The University of Berlin, Translated by Alexander Ogg University of Capetown, S.A. 3rd Edition
• Temperature is a measure of the ‘intensity of heat’
• Temperature:
- is a measure of the average kinetic energy of the constituent entities (say molecules)
- is the parameter which determines the distribution of species (say molecules) across various
energy states available.

• If two bodies, one of which feels warmer than the other, be brought together (for example, a
piece of heated metal and cold water), it is invariably found that the hotter body is cooled, and the
colder one is heated up to a certain point, and then all change ceases. The two bodies are then said
to be in thermal equilibrium
• Experience shows that such a state of equilibrium finally sets in, not only when two, but also when
any number of differently heated bodies are brought into mutual contact
A B C
A B C
If a body, A, be in thermal equilibrium with two other bodies, B
and C, then B and C are in thermal equilibrium with one another
A B C
Thermal Equilibrium

Zeroth law of thermodynamics - Axiom
• The so-called zeroth law of thermodynamics is the axiom which is probably most fundamental
• Formalized after the so-called first and second laws, and so it is called the zeroth law
Zeroth law of thermodynamics: When two bodies have equality of temperature with a third
body, then they have equality of temperature
The equivalent statement in mathematical logic is that if x = y and x = z, then y = z; this is in
fact equivalent to the first of Euclid’s common notions: things that are equal to the same thing
are also equal to each other
• Definition of the zeroth law enables the use of a thermometer as a measurement device
• A scale however needs to be defined.
• The old metric temperature scale, Celsius (C), was defined so that 0C is the freezing point of
water, and 100 C is the boiling point of water

• Enable us to compare the degree of heat of two bodies, B and C, without bringing them into
contact with one another
• Namely, by bringing each body into contact with an arbitrarily selected standard body, A (for
example, a mass of mercury enclosed in a vessel terminating in a fine capillary tube)
• By observing the volume of A in each case, it is possible to tell whether B and C are in thermal
equilibrium or not
• If they are not in thermal equilibrium, we can tell which of the two is the hotter
• A an arbitrarily selected normal volume, namely, the volume of A when in thermal equilibrium with
melting ice under atmospheric pressure
A SteamAIce
• This volumetric difference, which, by an appropriate choice of unit, is made to read 100 when A is
in contact with steam under atmospheric pressure is called the temperature in degrees
Centigrade with regard to A as thermometric substance
Two bodies of equal
temperature are, therefore, in
thermal equilibrium, and vice
versa
The temperature readings of no two thermometric substances agree, in general, except at 0nand 100
The definition of temperature is therefore somewhat arbitrary

• Permanent gases, in particular which are hard to condense, such as hydrogen,
oxygen, nitrogen, and carbon monoxide, and are taken as thermometric substances
• They agree almost completely within a considerable range of temperature, and
their readings are sufficiently in accordance for most purposes
• Besides, the coefficient of expansion of these different gases is the same, as
equal volumes of them expand under constant pressure by the same amount about
.
,/"
of their volume when heated from 0∘C to 1∘C
• Since, also, the influence of the external pressure on the volume of these gases
can be represented by a very simple law, we are led to the conclusion that
- these regularities are based on a remarkable simplicity in their constitution
- therefore, it is reasonable to define the common temperature given by them
simply as temperature.
- Consequently reduce the readings of other thermometers to those of
the gas thermometer

Thermodynamic Temperature Scale
• A temperature scale that is independent of the properties of any substance or substances is called
a thermodynamic temperature scale
• 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
A Triple Point Cell
Solid Ice, Liquid Water and
Water Vapor
Co-exist in thermal Equilibrium
By international Agreement the temperature of
this mixture has been defined to be 273.16K
Steam Point: A mixture of liquid water and water vapor (with no air)
in equilibrium at 1 atm pressure
Ice Point: A mixture of ice and water that is in equilibrium with air
saturated with vapor at 1 atm pressure

• The temperature scales used in the SI and in the English system
Celsius scale
(Swedish astronomer A. Celsius, 1702–1744)
On the Celsius scale, is defined so that 0∘C is the freezing point of water, and 100∘C is the boiling
point of water
Degree Celsius is commonly used in meteorological observation
Fahrenheit scale
(German instrument maker G. Fahrenheit, 1686–1736)
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
T(F) = 1.8T (C) + 32

The Celsius and Fahrenheit Scales
TC = T − 273.15

• Volume varies with pressure however, so different values would
be obtained on top of a mountain versus down in the valley, and
so this is not a good standard
• The modern Celsius scale is defined to be nearly the same, but
has
- 0.01 C as the so-called triple point of water
− 273.15 ◦C as absolute zero in K
• The triple point of water is defined at the state where three
phase of water (solid, liquid, and gas) are observed to co-exist
• The transformation between the absolute Kelvin scale and the
Celsius scale is given by
K = C + 273.15.
Celsius Scale

Kelvin Scale
• The thermodynamic temperature scale in the SI is the Kelvin scale, named after Lord Kelvin
• The temperature unit on this scale is the kelvin, which is designated by K
• The lowest temperature on the Kelvin scale is absolute zero, or 0 K
• A temperature scale that turns out to be nearly identical to the Kelvin scale is the ideal-gas
temperature scale
The Kelvin scale is related to the Celsius scale by
T(K) = T(C) + 273.15
T(R) = 1.8T(K)
• 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)
• The reference point was changed to a much more precisely reproducible point, the triple point of
water, which is assigned the value 273.16 K

Rankine scale
• The thermodynamic temperature scale in the English system is the Rankine scale, named after
William Rankine
• The temperature unit on this scale is the Rankine, which is designated by R
• The temperatures on this scale are measured using a constant-volume gas thermometer, which is
basically a rigid vessel filled with a gas, usually hydrogen or helium, at low pressure.
• This thermometer is based on the principle that “at low pressures, the temperature of a gas is
proportional to its pressure at constant volume”.
- The temperature of a gas of fixed volume varies linearly with pressure at sufficiently low
pressures
- Then the relationship between the temperature and the pressure of the gas in the vessel can be
expressed as T = a + bP constants a and b for a gas thermometer are determined experimentally
Once a and b are known, the temperature of a medium can be calculated from this relation by immersing the
rigid vessel of the gas thermometer into the medium and measuring the gas pressure when thermal
equilibrium is established between the medium and the gas in the vessel whose volume is held constant.
The Rankine scale is related to the Fahrenheit scale by
T(R) = T(F) + 459.67

• An ideal-gas temperature scale can be developed by
measuring the pressures of the gas in the vessel at two
reproducible points (such as the ice and the steam points)
and assigning suitable values to temperatures at those two
points
• Considering that only one straight line passes through two
fixed points on a plane, these two measurements are
sufficient to determine the constants a and b
• Then the unknown temperature T of a medium corresponding
to a pressure reading P can be determined from that
equation by a simple calculation
• The values of the constants will be different for each
thermometer, depending on the type and the amount of the
gas in the vessel, and the temperature values assigned at the
two reference points
• If the ice and steam points are assigned the values 0°C and
100°C, respectively, then the gas temperature scale will be
identical to the Celsius scale
Ideal Gas Temperature Scale

The Constant Volume Gas Thermometer
T = CpThe temperature of a body can be defined as , where p is the pressure in the bulb
Assuming at the triple point, we also have with the same constant C.
Therefore,
But only when the gas is of a very small amount, this measurement gives
consistent results among different materials used
This is called the ‘ideal gas temperature’.
Temperature T to be
measured

• In this case the value of the constant a (which corresponds to an absolute pressure of zero) is
determined to be -273.15°C regardless of the type and the amount of the gas in the vessel of the
gas thermometer
• This is the lowest temperature that can be obtained by a gas thermometer
• Thus we can obtain an absolute gas temperature scale by assigning a value of zero to the constant
a.
• In that case, T = bP, and thus we need to specify the temperature at only one point to define an
absolute gas temperature scale
- Absolute gas temperature scale is not a thermodynamic temperature scale, since it cannot be
used at very low temperatures (due to condensation) and at very high temperatures (due to
dissociation and ionization)
- Absolute gas temperature is identical to the thermodynamic temperature in the temperature
range in which the gas thermometer can be used
• Thus, we can view the thermodynamic temperature scale at this point as an absolute gas
temperature scale that utilizes an “ideal” or “imaginary” gas that always acts as a low-
pressure gas regardless of the temperature.
• If such a gas thermometer existed, it would read zero kelvin at absolute zero pressure,
which corresponds to -273.15°C on the Celsius scale

Thermodynamic properties

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