Substance Specific Heat Capacity at 25oC in J/go /K
The thermal energy needed to produce a temperature rise depends on the mass of the material, type of material (the molecular size and number of molecules per Kg.) and the temperature rise to which the material is subjected.
Thermal Energy Q= m c ∆t
For Gases there are two types of specific heats and they both have different values and it is better to distinguish them.
Specific Heat at constant Volume (CV): If one Kg of gas is supplied with an amount of heat energy sufficient to raise the temperature by 1K while the volume of the gas is kept constant, then the amount of heat energy supplied is known as the specific heat capacity at constant volume and is denoted by CV. Under these circumstances no work is done, but the gas has received an increase in internal energy U. The specific heat at constant volume for air is 718J/Kg/K.
Specific Heat at constant Pressure (CP):
If one Kg of gas is supplied with an amount of heat energy sufficient to raise the temperature by 1K while the pressure is held constant, then the amount of heat energy supplied is known as the specific heat capacity at constant volume and is denoted by CP.
This implies that when the gas has been heated it will expand a distance b, so work has been done.
Thus for the same amount of heat energy there has been an increase in internal energy U, plus work done. The value of CP is therefore greater than CV. The specific heat at constant
pressure for air is 1005/Kg/K.
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Expansion of Hydrogen gas at constant pressure.
In other more thermodynamics-based definitions, the relationship between the fixed mass of a gas at constant pressure is inversely proportional to the temperature applied to the system, which can be further used by stipulating a system where α represents cubic expansivity of a gas, with θ representing the temperature measured of the system in Kelvin:
Vα T
V = Vo (1 + α θ)
To maintain the constant, k, during heating of a gas at fixed pressure, the volume must increase. Conversely, cooling the gas decreases the volume. The exact value of the constant need not be known to make use of the law in comparison between two volumes of gas at equal pressure:
. Therefore, as temperature increases, the volume of the gas increases. Theoretically as a temperature reaches absolute zero the volume will also reach a point of zero.
Standard Conditions of Temperature and Pressure:The current version of IUPAC's standard is a temperature of 0 °C (273.15 K, 32 °F) and an absolute pressure of 100 kPa (14.504 psi), while NIST's (National Institute of Standards and Technology) version is a
temperature of 20 °C (293.15 K, 68 °F) and an absolute pressure of 101.325 kPa (14.696 psi).
The characteristic Gas equation: The ideal gas law is the equation of state of a hypothetical ideal gas,
The state of an amount of gas is determined by its pressure, volume, and temperature according to the equation:
PV=nRT
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The equation for latent heat is:
Q=mL
where: Q is the amount of energy released or absorbed during the change of phase of the substance (in joules), m is the mass of the substance, L is the specific latent heat for a particular substance (J kg-1).
In other words, specific latent heat is found when energy is divided by mass.
Latent heats and change of phase temps of common fluids and gases
Substance Latent Heat
Carbon dioxide 184 -57 574 -78
Helium 21 -268.93
Thermal Expansion of Solids and Liquids
Most solids and liquids expand when heated and contract when cooled. The thermal
expansion is usually small and unnoticeable. Nevertheless these expansions and contractions are important because the forces they exert are very great and must be compensated for in many structures such as railway lines, concrete roads and steel bridges.
When an iron rod is heated, the vibration of the molecules increases and their displacement or amplitude also increases. As the amplitude of vibration increases, the average distance between the molecules of the rod becomes larger and this accounts for its expansion in length.
Linear thermal expansion: The linear thermal expansion is the one-dimensional length change with temperature.
Application of thermal expansion:
• A glass jar will break if you fill it half-full of very hot water. The top and bottom of the jar want to be different sizes.
• Concrete roads and sidewalks are built in sections, with space left between the panels.
Otherwise, they would crack on very cold days and heave and buckle on very hot days.
• If the ocean becomes 1 degree (oF) warmer, its volume will increase by 0.01%. Since the ocean is several miles deep, this implies that the surface will rise about a foot, giving a change in the sea level. In the process, the beach line moves landwards 20 feet. People owning beach houses (or even living close to the ocean) find this alarming.
Anomalous Expansion of Water:
When water has become solid ice (below 0oC), its volume is considerably larger, and its density smaller. Hence ice floats in water.
Ice has a crystalline structure.
Normally the substances in the solid state occupy a smaller volume than in the liquid state. Due to the angular shape of the water molecules, ice has open-structured crystals. The forces binding water molecules together are strongest at certain angles. Ice in this open structure occupies a greater volume than it does in the liquid state.
Consequently, ice is less dense than water.
This behavior of water is of great importance in nature. The anomalous expansion of water has a favorable effect for animals living in water. Since the density of water is maximum at 40C, water at the bottom of lakes remains at 40C in winter even if the surface freezes. Water at the freezing point 0oC is less dense and so "floats". It means ice forms at the surface while the lake remains liquid below the ice. This allows marine animals to remain alive and move near the bottom.
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When a working fluid is a subject to a process, then the fluid will have started with one set of properties and ended with another, irrespective of how the process took place. For example, if a fluid within a system has an initial pressure (p1) and temperature (T1) and is then compressed producing an increase in pressure (p2) and temperature (T2), then we say that the fluid has undergone a process from state one to state two. We say that work is transferred in a thermodynamic system, if there is a
movement of the system boundaries.
Three types of thermodynamic systems are distinguished depending on the kinds of interaction and energy exchange taking place between the system and its surrounding environment:
• Isolated systems are completely isolated in every way from their environment. They do not exchange heat, work or matter with their environment. An example of an isolated system would be an insulated rigid container, such as an insulated gas cylinder.
• Closed systems are able to exchange energy (heat and work) but not matter with their environment. A greenhouse is an example of a closed system exchanging heat but not work with its environment. Whether a system exchanges heat, work or both is usually thought of as a property of its boundary. Example is cylinder and piston assembly of the internal combustion engine.
• Open systems: exchanging energy (heat and work) and matter with their environment.
A boundary allowing matter exchange is called permeable. The ocean would be an example of an open system. Example is gas turbine.
In reality, a system can never be absolutely isolated from its environment, because there is always at least some slight coupling, even if only via minimal gravitational attraction. In analyzing a system in steady-state, the energy into the system is equal to the energy leaving the system.
First law of thermodynamics: In thermodynamics, the first law of thermodynamics is an expression of the more universal physical law of the conservation of energy. “The increase in the internal energy of a system is equal to the amount of energy added by heating the system, minus the amount lost as a result of the work done by the system on its surroundings.”
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That is, it is impossible to extract energy by heat from a high-temperature energy source and then convert all of the energy into work. At least some of the energy must be passed on to heat a low-temperature energy sink. Thus, a heat engine with 100% efficiency is
thermodynamically impossible.
Thermodynamic processes: There are one or two processes which will help us to discuss the thermodynamic cycles of internal combustion engine and the gas turbine engine.
Reversible and irreversible processes:
A system is said to be reversible, when it changes from one state to another and at any instant during this process, an intermediate state point can be identified from any two properties that change as a result of the process. For reversibility, the fluid undergoing the process passes through a series of equilibrium states.
Irreversible Process
Reversible Process
In practice, because of energy transfers, the fluid undergoing a process cannot be kept in equilibrium in its intermediate states and a continuous path cannot be traced on a diagram of its properties. Such real processes are called Irreversible and they are usually represented by a dashed line joining the end states.
The seven most common thermodynamic processes are shown below:
1. An isobaric process occurs at constant pressure.
2. An isochoric process, or isometric/isovolumetric process, occurs at constant volume.
3. An isothermal process occurs at a constant temperature.
4. An adiabatic process occurs without loss or gain of heat.
5. An isentropic process (reversible adiabatic process) occurs at constant entropy.
6. An isenthalpic process occurs at a constant enthalpy.
7. A steady state process occurs without a change in the internal energy of a system.
Isochoric process: It is a process during which volume remains constant. The name is derived from the Greek isos, "equal", and khora, "place."
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but since pressure is constant, this means that
Applying the ideal gas law, this becomes
Assuming that the quantity of gas stays constant (e.g. no phase change during a chemical reaction). Since it is generally true that
then substituting the last two equations into the first equation produces:
.
The quantity in parentheses is equivalent to the molar specific heat for constant pressure:
c
p= c
V+ R
and if the gas involved in the isobaric process is monatomic then and . An isobaric process is shown on a P-V diagram as a straight horizontal line, connecting the initial and final thermostatic states. If the process moves towards the right, then it is an expansion. If the process moves towards the left, then it is a compression.
Enthalpy: An isochoric process is described by the equation Q = ∆U. It would be convenient to have a similar equation for isobaric processes. Substituting the second equation into the first yields
The quantity U + p V is a state function so that it can be given a name. It is called enthalpy, and is denoted as H. Therefore an isobaric process can be more succinctly described as
.
Isothermal Process: An isothermal process is a change in which the temperature of the system stays constant: ∆T = 0. This typically occurs when a system is in contact with an outside thermal reservoir (heat bath), and the change occurs slowly enough to allow the system to continually adjust to the temperature of the reservoir through heat exchange. An alternative special case in which a system exchanges no heat with its surroundings (Q = 0) is called an adiabatic process. In other words, in an isothermal process, the value ∆T = 0 but Q
≠ 0, while in an adiabatic process, ∆T ≠ 0 but Q = 0.
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Work done by expanding a gas:
Consider a piston and cylinder arrangement as shown in fig below, in which one Kg of a gas is contained at temperature TK. The piston has a cross sectional area of 1m2 is free to slide and rests on the gas, exerting a constant pressure by virtue of its weight.
Now let the temperature of the gas increase by 1K. This will produce an increase in volume and the piston will move to a new position. Let l (as lima) meters be the movement of the piston.
Expanding Gas.
Now work done = Force x Distance moved = F x l joules
= P x a x l
But a x l = change in volume
Work done = P (V2-V1), where V2= final volume
V1=initial volume If now, we consider incorporating the characteristic gas equation, PV= m RT, this becomes PV=RT for m=1Kg.
For the initial volume PV1= RT
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Two Stro
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A Typica
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Due to the variations required in temperatures and pressures, many different refrigerants are available. Refrigerators, air conditioners, and some heating systems are common applications that use this technology.
Refrigerants: Until the 1990s, the refrigerants were often chlorofluorocarbons such as R-12 (dichlorodifluoromethane), one in a class of several refrigerants using the brand name Freon, a trademark of DuPont. Its manufacture was discontinued in 1995 because of the damage that CFCs cause to the ozone layer if released into the atmosphere. One widely-adopted
replacement refrigerant is the hydrofluorocarbon (HFC) known as R-134a (1,1,1, 2-tetrafluoroethane). R-134a is not as efficient as the R-12 it replaced (in automotive
applications) and therefore, more energy is required to operate systems utilizing R-134a than those using R-12. Other substances such as liquid ammonia, or occasionally the less corrosive but flammable propane or butane, can also be used.
Since 2001, carbon dioxide, R-744, has increasingly been used, utilizing the transcritical cycle. In residential and commercial applications, the hydrochlorofluorocarbon (HCFC) R-22 is still widely used; however, HFC R-410a does not deplete the ozone layer and is being used more frequently. Hydrogen, helium, nitrogen, or plain air is used in the Stirling cycle,
providing the maximum number of options in environmentally friendly gases. More new refrigerators are now exploiting the R600A which is iso-butane, and does not deplete the ozone and is friendly to the environment.
Ideal properties of Refrigerant include:
¾ Be in-expansive and readily available
¾ Be non toxic, non corrosive, and present a low fire and explosion risk
¾ Working pressures should be above atmospheric temperatures but not too high
¾ Specific enthalpy of vaporization at the low temperature should be as high as possible
¾ Specific volume at compressor inlet should be as small as possible to keep the overall system mass down
¾ The refrigerant should not react with oil if the compressor is lubricated with oil in the refrigerant
The aircraft uses a heat pump/Refrigeration system (Air cycle Machine) which automatically cools or heats depending on the temperature requirement.
Heat of Combustion: During a chemical reaction chemicals may be formed or broken down into simpler units or elements. Such processes may be accompanied by heat being either received or expelled, during the reaction. This is known as the heat of reaction.
If the reaction takes place quickly and the element combines with oxygen, heat will be generated, known as the heat of combustion.
To determine, satisfactorily, the heat of combustion of a fuel an experimental method is often used, using an apparatus known as the bomb calorimeter. This measures the heat output of a known mass of the fuel, burnt in an adequate supply of oxygen i.e. Air. Hence the units of
‘heat of combustion’ are joules/Kg.
Optics i
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Nature of Light:
Light consists of electromagnetic waves. Electromsgnetic waves consists in turn of
oscillating Electric and Magnetic fields. These fields travel through space vibrating at right angles to each other and to the direction of motion.
Light waves are part of whole group of
electromagnetic waves or radiation, that includes X-rays, UV X-rays, Infra red rays and radio waves.
Light waves can be produced by the change of orbit of electrons inside atoms, and although each type of radiation has a different source they all have certain properties in common.
¾ They travle through space at 300,000Km/Sec i.e. the speed of light.
¾ They follow the realation v=fλ
¾ They carry energy from one space to another and an absorption cause an increase in temperature.
←
Frequency Decrease Frequency increase→
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A convex
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For concave (converging) mirrors, as long as the object is placed greater than one focal length in front of the mirror, a real image is produced. When the object is placed exactly one focal length in front of the mirror, no image is formed since the rays reflected from the mirror are parallel and can never intersect either in front of or behind the mirror. When the image is placed within one focal length of the mirror, a virtual, enlarged image is formed when the reflected, diverging rays, are "dotted back" behind the mirror. Concave spherical mirrors are considered to be positive mirrors since their mirrored surface faces "towards the center of the sphere".
For convex (diverging) mirrors, no matter when the object is placed in front of the mirror, a virtual, upright, reduced image is formed "behind the mirror" between F and V. Convex spherical mirrors are considered to be negative mirrors since their mirrored surface faces
"away from the center of the sphere".
Always remember, virtual images are formed by diverging rays; while real images are always formed by converging rays.
It is also important to be aware that mirrors can be classified according to the characteristics of the virtual images they form:
¾ Plane mirrors: virtual images are the same size as their objects
¾ Concave spherical mirrors: virtual images are larger that their objects
¾ Convex spherical mirrors: virtual images are smaller than their objects
Variation in the speed of light: the speed of light varies as it travels from medium to medium.
The refractive index gives the ratio of this speed change. Thus:
Refractive index = Speed of light in vacuum / Speed of light in medium
The above relationship implies that the greater the refractive index of the medium or the more the light is bent through the medium then the lower the speed of light.
Refraction of Light: when a ray of light is incident on the boundary separating the two mediums having different densities. A part of the light gets reflected and rest of the light changes its direction as it enters the second medium.
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Critical angle is that angle of incidence for which a ray of light while moving from a denser to a rarer medium just grazes over the surface of separation of the two media (that is, angle of refraction = 90o).
The conditions to be satisfied for total internal reflection to take place are
¾ The ray of light must travel from a denser medium to a rarer medium
¾ The angle of incidence must be greater than the critical angle for those two mediums Mirage and Looming:
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Principle of reversibility: The principle of reversibility states that light will follow exactly the same path if its direction of travel is reversed.
Lenses:
A lens is a portion of a transparent refracting medium bounded by two surfaces which are generally spherical or cylindrical or one curved and one plane surface. Basically, the lenses are classified as
1. Convex or Converging Lens 2. Concave or Diverging Lens
Convex Lens: A lens which is thicker in the middle and thinner at the edges is called a convex lens. In a convex lens at least one of its surfaces is bulging out at the middle.
According to their shapes the convex lenses
According to their shapes the convex lenses