Basic Concepts and Definitions - ITESM · (usually water at 4°C, for which ρ H2O = 1000 kg/m3)....

Basic Concepts and Definitions

Content

• Open and Close Systems• Properties of a System• State and Equilibrium• Processes and Cycles• Temperature and the Zeroth Law of Thermodynamics• Pressure

Open and Close Systems

System• A system is defined as a quantity of

matter or a region in space chosen for study.

• The mass or region outside the system is called the surroundings.

• The real or imaginary surface that separates the system from its surroundings is called the boundary.

• The boundary of a system can be fixed or movable.


• Systems may be considered to be closed or open, depending on whether a fixed mass or a fixed volume in space is chosen for study.

• A closed system (also known as a control mass) consists of a fixed amount of mass, and no mass can cross its boundary. That is, no mass can enter or leave a closed system. But energy, in the form of heat or work, can cross the boundary; and the volume of a closed system does not have to be fixed.

• If, as a special case, even energy is not allowed to cross the boundary, that system is called an isolated system.


• An open system, or a control volume, as it is often called, is a properly selected region in space.

• It usually encloses a device that involves mass flow such as a compressor, turbine, or nozzle.

• Flow through these devices is best studied by selecting the region within the device as the control volume.

• Both mass and energy can cross the boundary of a control volume.

Properties of a System

• Any characteristic of a system is called a property. Some familiar properties are pressure P, temperature T, volume V, and mass m.

• Properties are considered to be either intensive or extensive.• Intensive properties are those that are independent of the

mass of a system, such as temperature, pressure, and density.• Extensive properties are those whose values depend on the

size—or extent—of the system. Total mass, total volume, and total momentum are some examples of extensive properties.

• Extensive properties per unit mass are called specific properties. Some examples of specific properties are specific volume (v = V/m) and specific total energy (e = E/m).


• Density is defined as mass (m) per unit volume (V).ρ = m/V

• The reciprocal of density is the specific volume v, which is defined as volume (V) per unit mass (m).

v = V/m = 1/ρ

• As the density varies with temperature and pressure is specified for a value based of temperature 0°C or 15°C for liquids and 0°C for gases and standard pressure value that for gases is 1 atmosphere.


• Specific gravity, or relative density, is defined as the ratio of the density of a substance to the density of some standard substance at a specified temperature (usually water at 4°C, for which ρH2O = 1000 kg/m3).

SG = ρ/ρH2O

• Note that the specific gravity of a substance is a dimensionless quantity. However, in SI units, the numerical value of the specific gravity of a substance is exactly equal to its density in g/cm3 or kg/L (or 0.001 times the density in kg/m3) since the density of water at 4°C is 1 g/cm3 = 1 kg/L = 1000 kg/m3.


• The weight of a unit volume of a substance is called specific weightand is expressed as

γ = ρ g = w/V = mg/V (N/m3)

where g is the gravitational acceleration and w is the weight of the fluid (w = mg).


• Other units of measure density• API gravity (American Petroleum Institute) is a measure of how heavy or light a

petroleum liquid is compared to water. The formula to obtain API gravity of petroleum liquids, from relative density (RD), is:

API gravity = (141.5/RD at 15°C) - 131.5• Degrees Baumé (B°, Bé°). Before standardization on specific gravity around the time

of World War II the Baumé scale was generally used in industrial chemistry and pharmacology for the measurement of density of liquids. Today the Baumé scale is still used in various industries such as brewing, sugar beet processing, ophthalmic, starch industry, and winemaking.

Degrees Baumé = (140/RD at 15°C) - 130, for liquids less dense than waterDegrees Baumé = 145 - (145/RD at 15°C), for liquids more dense than water

• Degrees Brix (°Bx). It is the sugar content of an aqueous solution.Degrees Brix = % by weight of sugar in solution at 17.5 ° C


• Measuring the density of a solid1. The solid is weighed on a scale.2. The solid is immersed in water and while is

submerged it is reweighed in the balance.3. The volume is numerically equal to the

buoyancy, the difference between the two weight measurements.Archimedes Principle: “Any body immersed in a fluid experiences a buoyancy equal to the weight of the volume of liquid displaced”

4. Density formula appliesρ = mass / volume.


• Another way to measure the density of a solid1. The solid is weighed on a scale.2. The solid is placed in water and the water

displacement is measured. The displacement is equal to the volume of the solid.

3. Then density formula is appliedρ = mass / volume.


• Measure density of a fluid:• For a body in balance that floats on the surface of a liquid, we have

that the weight is equal to the buoyancymg = ρVg

• Known body mass and volume of the submerged part, we can determine the density of the liquid.

• A hydrometer is an instrument used to measure the specific gravity (or relative density) of liquids; that is, the ratio of the density of the liquid to the density of water.

• They have a graduated scale, which provide direct reading by the density of the liquid.

• The free liquid surface marks the value of the density scale hydrometer.

• Hydrometers may be calibrated for different uses, such as a lactometer for measuring the density (creaminess) of milk, a saccharometer for measuring the density of sugar in a liquid, or an alcoholometer for measuring higher levels of alcohol in spirits.


• Instruments for measuring the density• Hydrometers• Methods of differential pressure• Methods of displacement• Refractometer• Method of radiation• Method of boiling• Ultrasonic meter• Inertial measurement• Coriolis meter• Balance meter

State and Equilibrium

State• Consider a system not undergoing any change.• At this point, all the properties can be measured or

calculated throughout the entire system, which gives us a set of properties that completely describes the condition, or the state, of the system.

• At a given state, all the properties of a system have fixed values.

• If the value of even one property changes, the state will change to a different one.


Equilibrium• Thermodynamics deals with equilibrium states.• The word equilibrium implies a state of balance.• In an equilibrium state there are no unbalanced

potentials (or driving forces) within the system.• A system in equilibrium experiences no changes when it

is isolated from its surroundings.• There are many types of equilibrium, and a system is not

in thermodynamic equilibrium unless the conditions of all the relevant types of equilibrium are satisfied.

• For example, a system is in thermal equilibrium if the temperature is the same throughout the entire system.


• Mechanical equilibrium is related to pressure, and a system is in mechanical equilibrium if there is no change in pressure at any point of the system with time.

• If a system involves two phases, it is in phase equilibrium when the mass of each phase reaches an equilibrium level and stays there.

• A system is in chemical equilibrium if its chemical composition does not change with time, that is, no chemical reactions occur.

• A system will not be in equilibrium unless all the relevant equilibrium criteria are satisfied


The State Postulate• The state of a system is described by its properties.• But we know from experience that we do not need to specify

all the properties in order to fix a state.• Once a sufficient number of properties are specified, the rest

of the properties assume certain values automatically.• That is, specifying a certain number of properties is sufficient

to fix a state.• The number of properties required to fix the state of a system

is given by the state postulate:“The state of a simple compressible system is completely specified by two independent, intensive properties.”

• A system is called a simple compressible system in the absence of electrical, magnetic, gravitational, motion, and surface tension effects.

Processes and Cycles

Processes• Any change that a system undergoes from one equilibrium state

to another is called a process, and the series of states through which a system passes during a process is called the path of the process.

• To describe a process completely, one should specify the initial and final states of the process, as well as the path it follows, and the interactions with the surroundings.

• When a process proceeds in such a manner that the system remains infinitesimally close to an equilibrium state at all times, it is called a quasi-static, or quasi-equilibrium, process.

• A quasi-equilibrium process can be viewed as a sufficiently slow process that allows the system to adjust itself internally so that properties in one part of the system do not change any faster than those at other parts.


• The prefix iso- is often used to designate a process for which a particular property remains constant.

• An isothermal process, for example, is a process during which the temperature Tremains constant; an isobaric process is a process during which the pressure P remains constant; and an isochoric (or isometric) process is a process during which the specific volume v remains constant.


Cycles• A system is said to have undergone a cycle if it returns to its initial state at the

end of the process. That is, for a cycle the initial and final states are identical.

Rankine Cycle


The Steady-Flow Process• The terms steady and uniform are used frequently in

engineering, and thus it is important to have a clear understanding of their meanings.

• The term steady implies no change with time. The opposite of steady is unsteady, or transient.

• The term uniform, however, implies no change with location over a specified region.

• A large number of engineering devices operate for long periods of time under the same conditions, and they are classified as steady-flow devices.

• Processes involving such devices can be represented reasonably well by a somewhat idealized process, called the steady-flow process, which can be defined as a process during which a fluid flows through a control volume steadily.

Temperature and the Zeroth Law of Thermodynamics

Temperature• It originates from sense perceptions of man. It is a measure of molecular

activity.

K(kelvin)

°C(Celcius)

R(Rankine)

°F(Fahrenheit)

Water boils 373.15 100.00 671.67 212.00

Triple point of water

273.16 0.01 491.69 32.02

Water freezes 273.15 0.00 491.67 32.00

Absolute zero 0.00 -273.15 0.00 -459.67


Zeroth Law of Thermodynamics• 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.”


Thermometers• Temperature instruments use various phenomena that are influenced by

temperature and which include:a. changes in volume or in a state of bodies (solids, liquids or gases)b. change in resistance of a conductor (resistance probes)c. change in resistance of a semiconductor (thermistor)d. e.m.f. created at the junction of two different metals (thermocouple)e. intensity of the total radiation emitted by the body (radiation pyrometers)f. Other phenomena used by laboratories (speed of sound of a gas, the resonance

frequency of a crystal, etc.)


• Thus the following instruments were used:• Glass thermometers• Bimetallic Thermometers• Bulb and Capillary Thermometers• Thermocouples• Radiation pyrometers• Resistance Thermometers• Ultrasonic Thermometers• Quartz glass thermometers

Pressure

• Pressure is force per unit area applied in a direction perpendicular to the surface of an object.

Pressure = Force / Area

• Atmospheric pressure is the pressure of the atmosphere above the surface of the earth. Varies with height and at higher altitude, lower pressure.

• The formula for determining the average value of the pressure at different altitudes is (P→kPa, Z→m):

Pressure

• Pressure Concepts• Barometric pressure. Atmospheric

pressure is measured with the barometer.

• Gauge Pressure. Pressure is measured with the gauge or manometer.

• Vacuum Pressure. Negative gauge pressure.

• Absolute Pressure. A measure with respect to a zero pressure level.

Pressure

• Values of Average Sea Level Pressure (0°C)• 1 atm (atmosphere)• 14.696 pounds per square inch (lbf/in2)• 760 millimeters of mercury (mmHg)• 29.92 inches of mercury ("Hg) or (inHg)• 1.01325 x 105 N/m2

• 1.01325 x 105 Pascal (Pa)• 1.01325 bar• 1013.25 millibars (mb)

• 1 Pa = 1 N/m2 = 1 kg/ms2

Pressure

Mercury Barometer• The Italian Evangelista Torricelli (1608–1647) was the first to

conclusively prove that the atmospheric pressure can be measured by inverting a mercury-filled tube into a mercury container that is open to the atmosphere, as shown in the Figure.

• The pressure at point B is equal to the atmospheric pressure, and the pressure at C can be taken to be zero since there is only mercury vapor above point C and the pressure is very low relative to Patm and can be neglected to an excellent approximation.

• Writing a force balance in the vertical direction givesPatm = ρ g h

where ρ is the density of mercury, g is the local gravitational acceleration, and h is the height of the mercury column above the free surface.

• Note that the length and the cross-sectional area of the tube have no effect on the height of the fluid column of a barometer

Pressure

Variation of Pressure with Depth

Pressure

Pressure

Pascal’s law• A consequence of the pressure in a fluid

remaining constant in the horizontal direction is that the pressure applied to a confined fluid increases the pressure throughout by the same amount.

Pressure

Manometers

Pressure

• Other Pressure Measurement Devices

Pressure transducers

Examples (textbook)

EXAMPLE 1–1 Electric Power Generation by a Wind TurbineA school is paying $0.12/kWh for electric power. To reduce its power bill, the school installs a wind turbine with a rated power of 30 kW. If the turbine operates 2200 hours per year at the rated power, determine the amount of electric power generated by the wind turbine and the money saved by the school per year.

Examples (textbook)

Total Energy = (Power)(Time interval)= 30 kW 2,200 h/year= 𝟔𝟔𝟔𝟔,𝟎𝟎𝟎𝟎𝟎𝟎 𝐤𝐤𝐤𝐤𝐤𝐤/𝐲𝐲𝐲𝐲𝐲𝐲𝐲𝐲

Money saved = (Total Energy)(Unit cost of energy)= (66,000 kWh/year)($0.12/kWh)

Data:Unit cost of energy = $0.12/kWhPower = 30 kWTime interval = 2,200 h/year

= $𝟕𝟕,𝟗𝟗𝟗𝟗𝟎𝟎

Examples (textbook)

EXAMPLE 1–2 Obtaining Formulas from Unit ConsiderationsA tank is filled with oil whose density is ρ = 850 kg/m3. If the volume of the tank is V = 2 m3, determine the amount of mass m in the tank.

𝜌𝜌 =𝑚𝑚𝑉𝑉⇒ 𝑚𝑚 = 𝜌𝜌𝑉𝑉

𝑚𝑚 = 850kgm3 2 m3 = 𝟏𝟏,𝟕𝟕𝟎𝟎𝟎𝟎 𝐤𝐤𝐤𝐤

Examples (textbook)

EXAMPLE 1–3 The Weight of One Pound-MassUsing unity conversion ratios, show that 1.00 lbm weighs 1.00 lbf on earth.

𝑤𝑤 = 𝑚𝑚𝑚𝑚 = 1.00 lbm 32.174fts2

1 lbf

32.174 lbm � fts2

= 𝟏𝟏.𝟎𝟎𝟎𝟎 𝐥𝐥𝐥𝐥𝐥𝐥

Examples (textbook)

When you buy a box of breakfast cereal, the printing may say “Net weight: One pound (454 grams).” Technically, this means that the cereal inside the box weighs 1.00 lbf on earth and has a mass of 453.6 g (0.4536 kg). Using Newton’s second law, the actual weight of the cereal on earth is

𝑤𝑤 = 𝑚𝑚𝑚𝑚 = 453.6 g 9.81ms2

1 N

1 kg � ms2

1 kg1000 g

= 𝟒𝟒.𝟒𝟒𝟒𝟒𝟗𝟗 𝐍𝐍

Examples (textbook)

EXAMPLE 1– 4 Expressing Temperature Rise in Different UnitsDuring a heating process, the temperature of a system rises by 10°C. Express this rise in temperature in K, °F, and R.

∆𝑇𝑇 K = ∆𝑇𝑇 °C = 𝟏𝟏𝟎𝟎 𝐊𝐊

∆𝑇𝑇 °F = ∆𝑇𝑇 R = 𝟏𝟏𝟏𝟏 °𝐅𝐅

∆𝑇𝑇 R = 1.8∆𝑇𝑇 K = 𝟏𝟏𝟏𝟏 𝐑𝐑

Examples (textbook)

EXAMPLE 1–5 Absolute Pressure of a Vacuum ChamberA vacuum gage connected to a chamber reads 5.8 psi at a location where the atmospheric pressure is 14.5 psi. Determine the absolute pressure in the chamber.

𝑃𝑃abs = 𝑃𝑃atm − 𝑃𝑃vac= 14.5 psi − 5.8 psi= 𝟏𝟏.𝟕𝟕 𝐩𝐩𝐩𝐩𝐩𝐩

Examples (textbook)

EXAMPLE 1–6 Measuring Atmospheric Pressure with a BarometerDetermine the atmospheric pressure at a location where the barometric reading is 740 mmHg and the gravitational acceleration is g= 9.805 m/s2. Assume the temperature of mercury to be 10°C, at which its density is 13,570 kg/m3.

𝑃𝑃atm = 𝜌𝜌𝑚𝑚𝜌

= (13,570 kg/m3)(9.805 m/s2)(0.740 m)1 N

1 kg � m/s2

1 kPa1000 N/m2

= 𝟗𝟗𝟏𝟏.𝟓𝟓 𝐤𝐤𝐤𝐤𝐲𝐲

Examples (textbook)

EXAMPLE 1–7 Gravity Driven Flow from an IV BottleIntravenous infusions usually are driven by gravity by hanging the fluid bottle at sufficient height to counteract the blood pressure in the vein and to force the fluid into the body. The higher the bottle is raised, the higher the flow rate of the fluid will be. (a) If it is observed that the fluid and the blood pressures balance each other when the bottle is 1.2 m above the arm level, determine the gage pressure of the blood. (b) If the gage pressure of the fluid at the arm level needs to be 20 kPa for sufficient flow rate, determine how high the bottle must be placed. Take the density of the fluid to be 1020 kg/m3.

Examples (textbook)

a) Data:harm-bottle = 1.2 mρIV fluid = 1,020 kg/m3

Pgage, arm =?

𝑃𝑃gage, arm = 𝜌𝜌𝑚𝑚𝜌arm−bottle

= (1020 kg/m3)(9.81 m/s2)(1.20 m)1 kN

1000 kg � m/s2

1 kPa1 kN/m2

= 𝟏𝟏𝟗𝟗.𝟎𝟎 𝐤𝐤𝐤𝐤𝐲𝐲

Examples (textbook)

b) Data:Pgage-arm = 20 kPaρIV fluid = 1,020 kg/m3

harm-bottle = ?

𝑃𝑃gage, arm = 𝜌𝜌𝑚𝑚𝜌arm−bottle

⇒ 𝜌arm−bottle =𝑃𝑃gage, arm

𝜌𝜌𝑚𝑚

=20 kPa

(1020 kg/m3)(9.81 m/s2)1000 kg � m/s2

1 kN1 kN/m2

1 kPa

= 𝟗𝟗.𝟎𝟎𝟎𝟎𝐦𝐦

Examples (textbook)

EXAMPLE 1–9 Measuring Pressure with a ManometerA manometer is used to measure the pressure of a gas in a tank. The fluid used has a specific gravity of 0.85, and the manometer column height is 55 cm, as shown in Figure. If the local atmospheric pressure is 96 kPa, determine the absolute pressure within the tank.

Examples (textbook)Data:

SG = 0.85ρH2O = 1000 kg/m3

h = 55 cm = 0.55 mPatm = 96 kPaP = ?

SG =𝜌𝜌

𝜌𝜌H2O⇒ 𝜌𝜌 = SG 𝜌𝜌H2O = 0.85 1000

kgm3 = 850 kg/m3

𝑃𝑃 = 𝑃𝑃atm + 𝑃𝑃gage = 𝑃𝑃atm + 𝜌𝜌𝑚𝑚𝜌

= 96 kPa + (850 kg/m3)(9.81 m/s2)(0.55 m)1 N

1 kg � m/s2

1 kPa1000 N/m2

= 𝟏𝟏𝟎𝟎𝟎𝟎.𝟔𝟔 𝐤𝐤𝐤𝐤𝐲𝐲

Examples (textbook)

EXAMPLE 1–10 Measuring Pressure with a Multifluid ManometerThe water in a tank is pressurized by air, and the pressure is measured by a multifluid manometer as shown in Figure. The tank is located on a mountain at an altitude of 1400 m where the atmospheric pressure is 85.6 kPa. Determine the air pressure in the tank if h1 = 0.1 m, h2 = 0.2 m, and h3 = 0.35 m. Take the densities of water, oil, and mercury to be 1000 kg/m3, 850 kg/m3, and 13,600 kg/m3, respectively.

Examples (textbook)Data:

Patm = 85.6 kPah1 = 0.1 m, h2 = 0.2 m, h3 = 0.35 mρwater = 1000 kg/m3, ρoil = 850 kg/m3, ρmercury = 13600 kg/m3

P1 = ?

𝑃𝑃atm = 𝑃𝑃2 = 𝑃𝑃1 + 𝜌𝜌water𝑚𝑚𝜌1 + 𝜌𝜌oil𝑚𝑚𝜌2 + 𝜌𝜌mercury𝑚𝑚(−𝜌3)

⇒ 𝑃𝑃1 = 𝑃𝑃atm + 𝑚𝑚(𝜌𝜌mercury𝜌3 − 𝜌𝜌water𝜌1 − 𝜌𝜌oil𝜌2)

= 85.6 kPa + (9.81 m/s2)13600 kg

m3 0.35 m −1000 kg

m3 0.1 m −850 kg

m3 (0.2 m)1 N

1 kg�m/s21 kPa

1000 N/m2

= 𝟏𝟏𝟏𝟏𝟎𝟎 𝐤𝐤𝐤𝐤𝐲𝐲

Homework 1a

Problems from the textbook (Thermodynamics, Yunus, 8th ed.):• Choose 5 conceptual problems and answer them (those who you consider

to provide better understanding to the subject seen in this section)• Chapter 1, problems: 1-7, 18-29, 31-33, 40-44

• Choose 5 problems and answer them (those who you consider to provide better understanding to the subject seen in this section)

• Chapter 1, problems: 8-17, 30, 34-39, 45-81• What is the relative density of hydrogen at 100°C and 150,000 Pa?• If the density of gasoline is 6911.84 kg/m3, What is the relative density?• If the height of the Campus is 300 meters, what is it atmospheric pressure?

and in the moon?

Basic Concepts and Definitions

Basic Concepts and Definitions - ITESM · (usually water at 4°C, for which ρ H2O = 1000 kg/m3)....

Documents

Transcript of Basic Concepts and Definitions - ITESM · (usually water at 4°C, for which ρ H2O = 1000 kg/m3)....