thermodynamic properties

Thermodynamic Properties &

Measurement

Dr.RohitSinghLather

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 atstandard 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 thetransition 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 likesnow 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 MPa1 atm = 101325 Pa1 torr = 133.3 Pa

Static and Dynamic Pressure

The unit of pressure are Pa, psi, atm., bar, torr

force in newton or lbarea in m2 or in2

Dynamic PressurePressure 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.21 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

Pres

sure

Absolute Pressure

Gauge Pressure

Local atmosphericPressure reference

Gauge Pressure Suction/Vacuum

Gauge Pressure is relative pressure Absolute 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 PressurePressure 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 barVery 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 containswater, 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

Fluidwater/ 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.gP.A = Patm.A + m.g

So, Thus, P.A = PatmA + ρ.A.H.gP = Patm + ρ.g.H

∆P = P − Patm = Pgauge = ρ.g.H

m.g = ρ.V.gV 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 gaugepressure plus atmospheric pressure)

• Gauge pressure is zero referenced against ambient air pressure; it-the value-is equal to absolutepressure 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 hydrostaticforce 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 bedesigned 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 causescrescent to flex


Heat

• For quantitative purposes we utilize the change of volume which takes place in all bodies whenheated 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 bodygets hotter or colder, not merely by the sense of touch, but also by a purely mechanicalobservation affording a much greater degree of accuracy

• The conception of heat arises from that particular sensation of warmth or coldness which isimmediately 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, apiece of heated metal and cold water), it is invariably found that the hotter body is cooled, and thecolder one is heated up to a certain point, and then all change ceases. The two bodies are then saidto 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 CThermal 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 intocontact with one another

• Namely, by bringing each body into contact with an arbitrarily selected standard body, A (forexample, 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 thermalequilibrium 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 isin contact with steam under atmospheric pressure is called the temperature in degreesCentigrade 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 100The 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 thetemperature at which water freezes (or ice melts) and water exists as a solid–liquid mixture inequilibrium under standard atmospheric pressure (the ice point)

• The reference point was changed to a much more precisely reproducible point, the triple point ofwater, 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 bymeasuring the pressures of the gas in the vessel at tworeproducible points (such as the ice and the steam points)and assigning suitable values to temperatures at those twopoints

• Considering that only one straight line passes through twofixed points on a plane, these two measurements aresufficient to determine the constants a and b

• Then the unknown temperature T of a medium correspondingto a pressure reading P can be determined from thatequation by a simple calculation

• The values of the constants will be different for eachthermometer, depending on the type and the amount of thegas in the vessel, and the temperature values assigned at thetwo reference points

• If the ice and steam points are assigned the values 0°C and100°C, respectively, then the gas temperature scale will beidentical 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 bemeasured

• In this case the value of the constant a (which corresponds to an absolute pressure of zero) isdetermined to be -273.15°C regardless of the type and the amount of the gas in the vessel of thegas 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 todissociation and ionization)

- Absolute gas temperature is identical to the thermodynamic temperature in the temperaturerange in which the gas thermometer can be used

• Thus, we can view the thermodynamic temperature scale at this point as an absolute gastemperature 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

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