# How to use *Isothermal* in a sentence

The

**isothermal**surfaces are coaxial cylinders.I by the whole area B"DZ'VO under the

**isothermal**9"D and the adiabatic DZ', bounded by the axes of pressure and volume.The

**isothermal**lines, in fact, suggest that in the vast area of the Pacific something corresponding to the " planetary circulation " is established, further investigation of which may be of extreme value in relation to current inquiries concerning the upper air.It is often impossible to observe the pressure-coefficient dp/de directly, but it may be deduced from the

**isothermal**compressibility by means of the geometrically obvious relation, BE = (BEÃ†C) XEC. The ratio BEÃ†C of the diminution of pressure to the increase of volume at constant temperature, or - dp/dv, is readily observed.The difference 90-E is represented by the area 9"DdO to the left of the isometric Dd under the

**isothermal**B"D.AdvertisementA cycle such as ABCD enclosed by parts of two isothermals, BC, AD, and two adiabatics, AB, CD, is the simplest form of cycle for theoretical purposes, since all the heat absorbed, H', is taken in during the process represented by one

**isothermal**at the temperature o', and all the heat rejected, H", is given out during the process represented by the other at the temperature 0".Taking this ideal limit as a theoretical or absolute zero, the value of H may be represented on the diagram by the whole area included between the two adiabatics BAZ, CDZ' down to the points where they intersect the

**isothermal**of absolute zero, or the zero isopiestic OV asymptotically at infinity.Applying the above equation to a gas obeying the law pv=RT, for which the work done in

**isothermal**expansion from a volume i to a volume r is W=RT loger, whence dW=R log e rdt, he deduced the expression for the heat absorbed by a gas in**isothermal**expansion H=R log er/F'(t).This most fundamental point was finally settled by a more delicate test, devised by Lord Kelvin, and carried out in conjunction with Joule (1854), which showed that the fundamental assumption W =H in

**isothermal**expansion was very nearly true for permanent gases, and that F'(t) must therefore vary very nearly as J/T.Then by relations (2) the heat, H, absorbed in the

**isothermal**change BC, is to the work, W, done in the cycle ABCD in the ratio of o to (o' - o").AdvertisementIf we write K for the adiabatic elasticity, and k for the

**isothermal**elasticity, we obtain S/s = ECÃ†F = K/k.It is generally convenient to divide the path into two steps,

**isothermal**and isometric, or**isothermal**and isopiestic, and to integrate along each separately.The

**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.Joule failed to observe any change of temperature in his apparatus, and was therefore justified in assuming that the increase of intrinsic energy of a gas in

**isothermal**expansion was very small, and that the absorption of heat observed in a similar experiment in which the gas was allowed to do external work by expanding against the atmospheric pressure was equivalent to the external work done.A continual circulation might thus be set up in an

**isothermal**enclosure and maintained with the performance of an unlimited supply of work.AdvertisementIn considering the corresponding relation for a solution instead of a pure liquid, possible differences in concentration make the column method difficult of application, and it is better to attach the problem by means of an imaginary cycle of

**isothermal**operation.The stages at which heat is taken from the furnace and rejected to the cooler (C) are approximately

**isothermal**at the upper and lower limits of temperature respectively, and the cycle accordingly is approximately "perfect" in the thermodynamic sense.The theoretical indicator diagram is made up of two

**isothermal**lines for the taking in and rejection of heat, and two lines of constant volume for the two passages through the regenerator.It was then discharged through the regenerator, depositing heat for the next charge of air in turn to take up. The indicator diagram approximated to a form made up of two

**isothermal**lines and two lines of constant pressure.A further project, funded by the School, aims to develop methodologies for stability assessment of drugs using

**isothermal**calorimetry.AdvertisementIt will also include the analysis of dynamic light scattering,

**isothermal**titration calorimetry, and concepts for global analysis.If we write K for the adiabatic elasticity, and k for the

**isothermal**elasticity, we obtain S/s = ECÃƒâ€ F = K/k.It is often impossible to observe the pressure-coefficient dp/de directly, but it may be deduced from the

**isothermal**compressibility by means of the geometrically obvious relation, BE = (BEÃƒâ€ C) XEC. The ratio BEÃƒâ€ C of the diminution of pressure to the increase of volume at constant temperature, or - dp/dv, is readily observed.This assumption represents qualitatively the theoretical

**isothermal**of James Thomson (see Vaporization) and the phenomena of the critical state (see Condensation Of Gases); but the numerical results to which it leads differ so widely from experiment that it is necessary to suppose the constant, a, to be a function of the temperature.In virtue of relations (2), the change of entropy of a substance between any two states depends only on the initial and final states, and may be reckoned along any reversible path, not necessarily

**isothermal**, by dividing each small increment of heat, dH, by the temperature, 0, at which it is acquired, and taking the sum or integral of the quotients, dH/o, so obtained.AdvertisementIn the case of a solid or a liquid, the latent heat of

**isothermal**expansion may often be neglected, and if the specific heat, s, be also taken as constant, we have simply 0-00 =s log e0/00.In the special case, however, in which the transformation is conducted in an

**isothermal**enclosure, a common condition easily realized in practice, the temperature at the end of the transformation is reduced to its initial value throughout the substance.The 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.The function G is represented by the negative area D"DM under the

**isothermal**, bounded by the isopiestic DM and the axis of pressure.The available energy A is the work which may be gained from the system by a small reversible

**isothermal**operation with an osmotic cylinder, that is Pdv.AdvertisementThese

**isothermal**lines will be found to vary frommonth to month over the two hemispheres, or over local areas, during summer and winter, and their position is modified by continental or oceanic conditions.The temperature, however, has a daily range less than that of other countries under the same

**isothermal**lines.The heat absorbed in

**isothermal**expansion from vo to v at a temperature 0 is equal to the work done by equation (8) (since d0 =o, and 0(dp/d0)dv =pdv), and both are given by the expression RO log e (v/vo).