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adiabatic

Even if the expansion is adiabatic, in the sense that it takes place inside a non-conducting enclosure and no heat is supplied from external sources, it will not be isentropic, since the heat supplied by internal friction must be included in reckoning the change of entropy.

11If the substance in any state such as B were allowed to expand adiabatically (dH = o) down to the absolute zero, at which point it contains no heat and exerts no pressure, the whole of its available heat energy might theoretically be recovered in the form of external work, represented on the diagram by the whole area BAZcb under the adiabatic through the state-point B, bounded by the isometric Bb and the zero isopiestic bV.

00The increment of this area (or the decrement of the negative area E--04) at constant temperature represents the external work obtainable from the substance in isothermal expansion, in the same way that the decrement of the intrinsic energy represents the work done in adiabatic expansion.

00adiabatic nuclei approximation.

00adiabatic compression of gases and (alongside) oscillations in electronic circuits.

00adiabatic expansion.

00adiabatic flow of Newtonian fluids.

00adiabatic process is zero.

00adiabatic changes the amount of work required to produce a given change of state is independent of the way the work is done.

00For a gas, the adiabatic bulk modulus B = P, where P is the ambient pressure.

00That is to say, expansion is adiabatic and is continued down to the back pressure which in a non-condensing engine is 14.7 lb per square inch, since any back pressure above this amount is an imperfection which belongs to the actual engine.

00If the substance in any state such as B were allowed to expand adiabatically (dH = o) down to the absolute zero, at which point it contains no heat and exerts no pressure, the whole of its available heat energy might theoretically be recovered in the form of external work, represented on the diagram by the whole area BAZcb under the adiabatic through the state-point B, bounded by the isometric Bb and the zero isopiestic bV.

00If, starting from E, the same amount of heat h is restored at constant pressure, we should arrive at the point F on the adiabatic through B, since the substance has been transformed from B to F by a reversible path without loss or gain of heat on the whole.

00EF is the change of volume corresponding to a change of pressure BE when no heat is allowed to escape and the path is the adiabatic BF, EC is the change of volume for the same change of pressure BE when the path is the isothermal BC. These changes of volume are directly as the compressibilities, or inversely as the elasticities.

00If we write K for the adiabatic elasticity, and k for the isothermal elasticity, we obtain S/s = ECÃƒâ€ F = K/k.

00along the adiabatic, which can be integrated, giving the equations to the adiabatics, provided that the values of the specific heats and expansion-coefficients are known.

00The isothermal elasticity - v(dp/dv) is equal to the pressure p. The adiabatic elasticity is equal to y p, where -y is the ratio S/s of the specific heats.

00In thiscase the ratio of the specific heats is constant as well as the difference, and the adiabatic equation takes the simple form, pv v = constant, which is at once obtained by integrating the equation for the adiabatic elasticity, - v(dp/dv) =yp.

00If we assume that s is a linear function of 0, s= so(I +aO), the adiabatic equation takes the form, s 0 log e OW +aso(0 - Oo) +R loge(v/vo) =o

00(14) where (00,v), (e 0, vo) are any two points on the adiabatic. The corresponding expressions for the change of energy or total heat are obtained by adding the term 2as 0 (02-002) to those already given, thus: E - Eo = so (0-00) + 2 aso (02-002), F - Fo=S0(0-00) + zaso (02-002), where So= so+R.

00- It follows from the definition of the absolute scale of temperature, as given in relations (2), that in passing at constant temperature 0 from one adiabatic 4' (Fig.

00I) to any other adiabatic 0", the quotient H/o of the heat absorbed by the temperature at which it is absorbed is the same for the same two adiabatics whatever the temperature of the isothermal path.

00In passing along an adiabatic there is no change of entropy, since no heat is absorbed.

00Even if the expansion is adiabatic, in the sense that it takes place inside a non-conducting enclosure and no heat is supplied from external sources, it will not be isentropic, since the heat supplied by internal friction must be included in reckoning the change of entropy.

00If the tube is a perfect non-conductor, and if there are no eddies or frictional dissipation, the state of the substance at any point of the tube as to E, p, and v, is represented by the adiabatic or isentropic path, dE= -pdv.

00I by the whole area B"DZ'VO under the isothermal 9"D and the adiabatic DZ', bounded by the axes of pressure and volume.

00The intrinsic energy, E, is similarly represented by the area DZ'Vd under the adiabatic to the right of the isometric Dd.

00The increment of this area (or the decrement of the negative area E--04) at constant temperature represents the external work obtainable from the substance in isothermal expansion, in the same way that the decrement of the intrinsic energy represents the work done in adiabatic expansion.

00K, k, Adiabatic and isothermal elasticities.

00That is to say, instead of using Boyle's law, which supposes that the pressure changes so exceedingly slowly that conduction keeps the temperature constant, we must use the adiabatic relation p = kpy, whence d p /d p = y k p Y 1= yp/p, and U = (yp/p) [Laplace's formula].

00142) showed that a very small departure from the adiabatic condition would lead to a stifling of the sound quite out of accord with observation.

00Assuming, however, that the agreement is close enough for practical requirement, the conbustion of the cordite may be considered complete at this stage P, and in the subsequent expansion it is assumed that the gas obeys an adiabatic law in which the pressure varies inversely as some mtn power of the volume.

00The Direct Methods Of Measuring The Ratio S/S, By The Velocity Of Sound And By Adiabatic Expansion, Are Sufficiently Described In Many Text Books.

00(See Thermodynamics and Steam-Engine.) In Carnot's cycle the substance takes in heat at its highest temperature, then passes by adiabatic expansion from the top to the bottom of its temperature range, then rejects heat at the bottom of the range, and is finally brought back by adiabatic compression to the highest temperature at which it again takes in heat, and so on.

00Stirling substituted for the two stages of adiabatic expansion and compression the passage of the air to and fro through a "regenerator," in which the air was alternately cooled by storing its heat in the material of the regenerator and reheated by picking the stored heat up again on the return journey.

0010, P. 349, 1867) investigated the form of the adiabatic for steam passing through the state p= 760 mm., 0=373Ã‚° Abs., by observing the pressure of superheated steam at any temperature which just failed to produce a cloud on sudden expansion to atmospheric pressure.

00The assumption n=s/R simplifies the adiabatic equation, but the value n=3.5 gives So =0.497 at zero pressure, which was the value found by Callendar experimentally at 108Ã‚° C. and 1 atmosphere pressure.

00A vapour compression machine does not, however, work precisely in the reversed Carnot cycle, inasmuch as the fall in temperature between the condenser and the refrigerator is not produced, nor is it attempted to be produced, by the adiabatic expansion of the agent, but results from the evaporation of a portion of the liquid itself.

00If, starting from E, the same amount of heat h is restored at constant pressure, we should arrive at the point F on the adiabatic through B, since the substance has been transformed from B to F by a reversible path without loss or gain of heat on the whole.

01EF is the change of volume corresponding to a change of pressure BE when no heat is allowed to escape and the path is the adiabatic BF, EC is the change of volume for the same change of pressure BE when the path is the isothermal BC. These changes of volume are directly as the compressibilities, or inversely as the elasticities.

01along the adiabatic, which can be integrated, giving the equations to the adiabatics, provided that the values of the specific heats and expansion-coefficients are known.

01The isothermal elasticity - v(dp/dv) is equal to the pressure p. The adiabatic elasticity is equal to y p, where -y is the ratio S/s of the specific heats.

01In thiscase the ratio of the specific heats is constant as well as the difference, and the adiabatic equation takes the simple form, pv v = constant, which is at once obtained by integrating the equation for the adiabatic elasticity, - v(dp/dv) =yp.

01If we assume that s is a linear function of 0, s= so(I +aO), the adiabatic equation takes the form, s 0 log e OW +aso(0 - Oo) +R loge(v/vo) =o

01(14) where (00,v), (e 0, vo) are any two points on the adiabatic. The corresponding expressions for the change of energy or total heat are obtained by adding the term 2as 0 (02-002) to those already given, thus: E - Eo = so (0-00) + 2 aso (02-002), F - Fo=S0(0-00) + zaso (02-002), where So= so+R.

01I) to any other adiabatic 0", the quotient H/o of the heat absorbed by the temperature at which it is absorbed is the same for the same two adiabatics whatever the temperature of the isothermal path.

01In passing along an adiabatic there is no change of entropy, since no heat is absorbed.

01If the tube is a perfect non-conductor, and if there are no eddies or frictional dissipation, the state of the substance at any point of the tube as to E, p, and v, is represented by the adiabatic or isentropic path, dE= -pdv.

01I by the whole area B"DZ'VO under the isothermal 9"D and the adiabatic DZ', bounded by the axes of pressure and volume.

01The intrinsic energy, E, is similarly represented by the area DZ'Vd under the adiabatic to the right of the isometric Dd.

01K, k, Adiabatic and isothermal elasticities.

01That is to say, instead of using Boyle's law, which supposes that the pressure changes so exceedingly slowly that conduction keeps the temperature constant, we must use the adiabatic relation p = kpy, whence d p /d p = y k p Y 1= yp/p, and U = (yp/p) [Laplace's formula].

01142) showed that a very small departure from the adiabatic condition would lead to a stifling of the sound quite out of accord with observation.

01Assuming, however, that the agreement is close enough for practical requirement, the conbustion of the cordite may be considered complete at this stage P, and in the subsequent expansion it is assumed that the gas obeys an adiabatic law in which the pressure varies inversely as some mtn power of the volume.

01The Direct Methods Of Measuring The Ratio S/S, By The Velocity Of Sound And By Adiabatic Expansion, Are Sufficiently Described In Many Text Books.

0110, P. 349, 1867) investigated the form of the adiabatic for steam passing through the state p= 760 mm., 0=373° Abs., by observing the pressure of superheated steam at any temperature which just failed to produce a cloud on sudden expansion to atmospheric pressure.

01The assumption n=s/R simplifies the adiabatic equation, but the value n=3.5 gives So =0.497 at zero pressure, which was the value found by Callendar experimentally at 108° C. and 1 atmosphere pressure.

01A vapour compression machine does not, however, work precisely in the reversed Carnot cycle, inasmuch as the fall in temperature between the condenser and the refrigerator is not produced, nor is it attempted to be produced, by the adiabatic expansion of the agent, but results from the evaporation of a portion of the liquid itself.

01If we write K for the adiabatic elasticity, and k for the isothermal elasticity, we obtain S/s = ECÃ†F = K/k.

02

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