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Encyclopedia > Adiabatic process

In thermodynamics, an adiabatic process or an isocaloric process is a thermodynamic process in which no heat is transferred to or from the working fluid. The term "adiabatic" literally means impassable (from a dia bainein), corresponding here to an absence of heat transfer. For example, an adiabatic boundary is a boundary that is impermeable to heat transfer and the system is said to be adiabatically (or thermally) insulated; an insulated wall approximates an adiabatic boundary. Another example is the adiabatic flame temperature, which is the temperature that would be achieved by a flame in the absence of heat loss to the surroundings. An adiabatic process that is reversible is also called an isentropic process. Thermodynamics (from the Greek θερμη, therme, meaning heat and δυναμις, dunamis, meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ... A thermodynamic process may be defined as the energetic evolution of a thermodynamic system proceeding from an initial state to a final state. ... For other uses, see Heat (disambiguation) In physics, heat, symbolized by Q, is energy transferred from one body or system to another due to a difference in temperature. ... A fluid is defined as a substance that continually deforms (flows) under an applied shear stress regardless of the magnitude of the applied stress. ... In thermal physics, heat transfer is the passage of thermal energy from a hot to a cold body. ... In the study of combustion, there are two types of adiabatic flame temperature depending on how the process is completed: constant volume and constant pressure. ... For other uses, see Fire (disambiguation). ... In thermodynamics, a reversible process (or reversible cycle if the process is cyclic) is a process that can be reversed by means of infinitesimal changes in some property of the system. ... An isentropic process (a combination of the Greek word iso -same- and entropy) is one during which the entropy of working fluid remains constant. ...


The opposite extreme -- of maximum heat transfer with the surroundings, causing the temperature to remain constant -- is known as an isothermal process. Since temperature is thermodynamically conjugate to entropy, the isothermal process is conjugate to the adiabatic process for reversible transformations. An isothermal process is a thermodynamic process in which the temperature of the system stays constant: ΔT = 0. ... Thermodynamic potentials Maxwell relations Bridgmans equations Exact differential (edit) In thermodynamics, the internal energy of a system is expressed in terms of pairs of conjugate variables such as pressure/volume or temperature/entropy. ...


A transformation of a thermodynamic system can be considered adiabatic when it is quick enough that no significant heat is transferred between the system and the outside. The adiabatic process can also be called quasi-static. At the opposite, a transformation of a thermodynamic system can be considered isothermal if it is slow enough so that the system's temperature remains constant by heat exchange with the outside. In thermodynamics a quasistatic process is a process that happens infinitely slowly. ...

Contents

Adiabatic heating and cooling

Adiabatic heating and cooling are processes that commonly occur due to a change in the pressure of a gas. Adiabatic heating occurs when the pressure of a gas is increased. An example of this is what goes on in a bicycle pump. After using a pump to inflate a pneumatic tire or ball, the barrel of the pump is found to have heated up as a result of adiabatic heating. Diesel engines rely on adiabatic heating during their compression stroke to elevate the temperature sufficiently to ignite the fuel. Adiabatic heating also occurs in the Earth's atmosphere when an air mass descends, for example, in a katabatic wind or Foehn wind flowing downhill. This article is about pressure in the physical sciences. ... This article does not cite any references or sources. ... Bicycle Floor Pump Foot operated bike pump Frame mounted bike pump A bicycle pump is a type of positive-displacement pump specifically designed for inflating balls (basket,soccer). ... The diesel engine is a type of internal combustion engine; more specifically, a compression ignition engine, in which the fuel is ignited by the high temperature of a compressed gas, rather than a separate source of energy (such as a spark plug). ... “Air” redirects here. ... In meteorology, an air mass is a large volume of air having fairly uniform characteristics of temperature, atmospheric pressure, and water vapor content. ... A katabatic wind, from the Greek word katabatikos meaning going downhill, is a wind that blows down a topographic incline such as a hill, mountain, or glacier. ... A foehn wind occurs when a deep layer of prevailing wind is forced over a mountain range. ...


Adiabatic cooling occurs when the pressure of a substance is decreased, such as when it expands into a larger volume. An example of this is when the air is released from a pneumatic tire; the outlet air will be noticeably cooler than the tire. Adiabatic cooling does not have to involve a fluid. One technique used to reach very low temperatures (thousandths and even millionths of a degree above the theory of absolute zero) is adiabatic demagnetisation, where the change in magnetic field on a magnetic material is used to provide adiabatic cooling. Adiabatic cooling also occurs in the Earth's atmosphere with orographic lifting and lee waves, and this can form pileus or lenticular clouds if the air is cooled below the dew point. Adiabatic demagnetization is a technique for attaining temperatures well below 1 kelvin. ... Magnetic field lines shown by iron filings In physics, a magnetic field is a solenoidal vector field in the space surrounding moving electric charges and magnetic dipoles, such as those in electric currents and magnets. ... “Air” redirects here. ... This wave cloud pattern formed off of the Île Amsterdam in the far southern Indian Ocean, due to orographic lift of an airmass by the island, producing alternating bands of condensed and invisible humidity downwind of the island as the moist air moves in vertical waves and the moisture successively... Categories: Aeronautics | Meteorology | Stub ... A pileus (Latin for cap) is a small, horizontal cloud that can appear above a cumulus or cumulonimbus cloud, giving the parent cloud a characteristic hoodlike appearance. ... Lenticular clouds, technically known as altocumulus standing lenticularis, are stationary lens-shaped clouds that form at high altitudes, normally aligned at right-angles to the wind direction. ... Dew on a spider web The dew point (or dewpoint) of a given parcel of air is the temperature to which the parcel must be cooled, at constant barometric pressure, for water vapor to condense into water, called dew. ...


Such temperature changes can be quantified using the ideal gas law, or the hydrostatic equation for atmospheric processes. Isotherms of an ideal gas The ideal gas law is the equation of state of a hypothetical ideal gas, first stated by Benoît Paul Émile Clapeyron in 1834. ... Table of Hydraulics and Hydrostatics, from the 1728 Cyclopaedia. ...


It should be noted that no process is truly adiabatic. Many processes are close to adiabatic and can be easily approximated by using an adiabatic assumption, but there is always some heat loss. There is no such thing as a perfect insulator.


Ideal gas

For a simple substance, during an adiabatic process in which the volume increases, the internal energy of the working substance must necessarily decrease
For a simple substance, during an adiabatic process in which the volume increases, the internal energy of the working substance must necessarily decrease

The mathematical equation for an ideal fluid undergoing an adiabatic process is Image File history File links This is a lossless scalable vector image. ... Image File history File links This is a lossless scalable vector image. ... In thermodynamics, the internal energy of a thermodynamic system, or a body with well-defined boundaries, denoted by U, or sometimes E, is the total of the kinetic energy due to the motion of molecules (translational, rotational, vibrational) and the potential energy associated with the vibrational and electric energy of... An ideal gas or perfect gas is a hypothetical gas consisting of identical particles of zero volume, with no intermolecular forces. ...

 P V^{gamma} = operatorname{constant} qquad

where P is pressure, V is volume, and

 gamma = {C_{P} over C_{V}} = frac{alpha + 1}{alpha},

CP being the specific heat for constant pressure and CV being the specific heat for constant volume. α comes from the number of degrees of freedom divided by 2 (3/2 for monatomic gas, 5/2 for diatomic gas). For a monatomic ideal gas, γ = 5 / 3, and for a diatomic gas (such as nitrogen and oxygen, the main components of air) γ = 7 / 5. Note that the above formula is only applicable to classical ideal gases and not Bose-Einstein or Fermi gases. The specific heat capacity (symbol c or s, also called specific heat) of a substance is defined as heat capacity per unit mass. ... General Name, symbol, number nitrogen, N, 7 Chemical series nonmetals Group, period, block 15, 2, p Appearance colorless gas Standard atomic weight 14. ... General Name, Symbol, Number oxygen, O, 8 Chemical series nonmetals, chalcogens Group, Period, Block 16, 2, p Appearance colorless (gas) very pale blue (liquid) Standard atomic weight 15. ... “Air” redirects here. ...


For adiabatic processes, it is also true that

 P^{gamma-1}T^{-gamma}= operatorname{constant}
 VT^alpha = operatorname{constant}

where T is temperature in kelvins.


This can also be written as

 TV^{gamma - 1} = operatorname{constant}

Derivation of continuous formula

The definition of an adiabatic process is that heat transfer to the system is zero, δQ = 0. Then, according to the first law of thermodynamics, The first law of thermodynamics, a generalized expression of the law of the conservation of energy, states: // Description Essentially, the First Law of Thermodynamics declares that energy is conserved for a closed system, with heat and work being the forms of energy transfer. ...

 text{(1)} qquad d U + delta W = delta Q = 0

where dU is the change in the internal energy of the system and δW is work done by the system. Any work (δW) done must be done at the expense of internal energy U, since no heat δQ is being supplied from the surroundings. Pressure-volume work δW done by the system is defined as

 text{(2)} qquad delta W = P , dV.

However, P does not remain constant during an adiabatic process but instead changes along with V.


It is desired to know how the values of dP and dV relate to each other as the adiabatic process proceeds. For an ideal gas the internal energy is given by

 text{(3)} qquad U = alpha n R T

where R is the universal gas constant and n is the number of moles in the system (a constant). Molar gas constant (also known as universal gas constant, usually denoted by symbol R) is the constant occurring in the universal gas equation, i. ...


Differentiating Equation (3) and use of the ideal gas law yields Isotherms of an ideal gas The ideal gas law is the equation of state of a hypothetical ideal gas, first stated by Benoît Paul Émile Clapeyron in 1834. ...

 text{(4)} qquad d U = alpha n R , dT = alpha , d (P V) = alpha (P , dV + V , dP).

Equation (4) is often expressed as  d U = n C_{V} , d T because CV = αR.


Now substitute equations (2), (3), and (4) into equation (1) to obtain

 -P , dV = alpha P , dV + alpha V , dP ,

simplify,

 - (alpha + 1) P , dV = alpha V , dP ,

divide both sides by PV,

 -(alpha + 1) {d V over V} = alpha {d P over P}.

After integrating the left and right sides from Vo to V and from Po to P and changing the sides respectively,

 ln left( {P over P_0} right) = {-{alpha + 1 over alpha}} ln left( {V over V_0} right).

Exponentiate both sides,

 left( {P over P_0} right) = left( {V over V_0} right)^{-{alpha + 1 over alpha}},

eliminate the negative sign,

 left( {P over P_0} right) = left( {V_0 over V} right)^{alpha + 1 over alpha}.

Therefore

 left( {P over P_0} right) left( {V over V_0} right)^{alpha+1 over alpha} = 1

and

 P V^{alpha+1 over alpha} = P_0 V_0^{alpha+1 over alpha} = P V^gamma = operatorname{constant}.

Derivation of discrete formula

The change in internal energy of a system, measured from state 1 to state 2, is equal to

 text{(1)} qquad delta U = alpha R n_2T_2 - alpha R n_1T_1 = alpha R (n_2T_2 - n_1T_1)

At the same time, the work done by the pressure-volume changes as a result from this process, is equal to

 text{(2)} qquad delta W = P_2V_2 - P_1V_1

Since we require the process to be adiabatic, the following equation needs to be true

 text{(3)} qquad delta U + delta W = 0

Substituting (1) and (2) in (3) leads to

 alpha R (n_2T_2 - n_1T_1) + (P_2V_2 - P_1V_1) = 0 qquad qquad qquad

or

 frac {(P_2V_2 - P_1V_1)} {-(n_2T_2 - n_1T_1)} = alpha R qquad qquad qquad

If it's further assumed that there are no changes in molar quantity (as often in practical cases), the formula is simplified to this one:

 frac {(P_2V_2 - P_1V_1)} {-(T_2 - T_1)} = alpha n R qquad qquad qquad

Graphing adiabats

An adiabat is a curve of constant entropy on the P-V diagram. Properties of adiabats on a P-V diagram are:

  1. Every adiabat asymptotically approaches both the V axis and the P axis (just like isotherms).
  2. Each adiabat intersects each isotherm exactly once.
  3. An adiabat looks similar to an isotherm, except that during an expansion, an adiabat loses more pressure than an isotherm, so it has a steeper inclination (more vertical).
  4. If isotherms are concave towards the "north-east" direction (45 °), then adiabats are concave towards the "east north-east" (31 °).
  5. If adiabats and isotherms are graphed severally at regular changes of entropy and temperature, respectively (like altitude on a contour map), then as the eye moves towards the axes (towards the south-west), it sees the density of isotherms stay constant, but it sees the density of adiabats grow. The exception is very near absolute zero, where the density of adiabats drops sharply and they become rare (see Nernst's theorem).

The following diagram is a P-V diagram with a superposition of adiabats and isotherms: The third law of thermodynamics was developed by Walther Nernst and is thus sometimes referred to as Nernsts theorem. ...


Image:Entropyandtemp.PNG Superposition of Entropy and Temperature Contour Maps (on a P-V diagram). ...


The isotherms are the red curves and the adiabats are the black curves. The adiabats are isentropic. Volume is the abscissa (horizontal axis) and pressure is the ordinate (vertical axis). Abscissa means the x coordinate on an (x, y) graph; the input of a mathematical function against which the output is plotted. ... Ordinate means the y coordinate on an (x, y) graph; the plotted output of a mathematical function. ...


See also

Cameron likes supras A cyclic process is a thermodynamic process which begins from and finishes at the same thermostatic state. ... The first law of thermodynamics, a generalized expression of the law of the conservation of energy, states: // Description Essentially, the First Law of Thermodynamics declares that energy is conserved for a closed system, with heat and work being the forms of energy transfer. ... An isobaric process is a thermodynamic process in which the pressure stays constant; . The heat transferred to the system does work but also changes the internal energy of the system: according to the first law of thermodynamics, where W is work done by the system, E is internal energy, and... Isochoric Process in the PV-diagram An isochoric process, also called an isometric process or an isovolumetric process, is a thermodynamic process in which the volume stays constant; . This implies that the process does no pressure-volume work, since such work is defined by , where P is pressure (no minus... An isothermal process is a thermodynamic process in which the temperature of the system stays constant: ΔT = 0. ... A polytropic process is a thermodynamic process that a system undergoes that obeys the relation , where p is pressure, V is volume, n is any real number (polytropic exponent), and K is a constant. ... For other uses of the term entropy, see Entropy (disambiguation) The thermodynamic entropy S, often simply called the entropy in the context of thermodynamics, is a measure of the amount of energy in a physical system that cannot be used to do work. ... Quasistatic equilibrium is the quasi-balanced state of a thermodynamic system near to equilibrium in some sense or degree. ... This article lacks information on the importance of the subject matter. ...


  Results from FactBites:
 
Adiabatic process - Wikipedia, the free encyclopedia (986 words)
Another example is the adiabatic flame temperature, which is the temperature that would be achieved by a flame in the absence of heat loss to the surroundings.
Since temperature is thermodynamically conjugate to entropy, the isothermal process is conjugate to the adiabatic process for reversible transformations.
Adiabatic heating and cooling are processes that commonly occur due to a change in the pressure of a gas.
Cyclic process - Wikipedia, the free encyclopedia (827 words)
A cyclic process is a thermodynamic process which begins from and finishes at the same thermostatic state.
Equation (1) makes a cyclic process similar to an isothermal process: even though the internal energy changes during the course of the cyclic process, when the cyclic process finishes the system's energy is the same as the energy it had when the process began.
The adiabatic processes are impermeable to heat: heat flows into the loop through the left pressurizing process and some of it flows back out through the right depressurizing process, and the heat which remains does the work.
  More results at FactBites »

 
 

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