Temperature perfect gas

The thermodynamic temperature scale T is defined by the second law of thermodynamics. It can be shown that the thermodynamic temperature scale is identical with the perfect-gas temperature scale defined as follows ... 

P3.21 The thermodynamic temperature scale defines a temperature T (where the superscript a is used to distinguish this absolute thermodynamic temperature from the perfect gas temperature) in terms of the reversible heat flows of a heat engine operating between it and an arbitrary fixed temperature (eqn 3.11)... 

The problem asks us to show that the thermodynamic and perfect gas temperatures differ by at most a constant numerical factor. That amounts to showing that... 

As Section 3.2(b) shows, the efficiency of any reversible heat engine (including one that uses a perfect gas as a working fluid) is the same, and therefore the ratio of heat flows to the two reservoirs is the same. That is, the ratio — is the same in the expression for the perfect-gas temperature ratio and the... 

It can also be readily shown that the thermodynamic temperature, as defined by (1 12), is the same as the perfect gas temperature. (See Ftoblem 8 on p. 69.) However, it will be recognized that this coincidence plays no essential role in thermodynamics— the basic theory can be developed, as in the present chapter, without any reference to the existence of perfect gases. 

A perfect gas is a fluid which satisfies the conditions (a) its temperature 6 is proportional to pF (6) its internal energy depends only on the temperature. By performing a Carnot cycle on such a gas, prove that the perfect gas temperature 6 is proportional to the thermod3mamic temperature T, as defined in 1-11. 

The deviation from the perfect gas law is not great at ordinary pressures and temperatures. At the highest pressure normally encountered commercially, 41 MPa (6000 psig), the compressibiUty factor of nitrogen is 1.3629 at 25°C (12). 

The temperature obeys the adiabatic flow equation for a perfect gas. 

The gas usually deviates considerably from the perfect-gas laws, and in many cases temperature or other limitations necessitate a thor-... 

Compressibility of Natural Gas All gases deviate from the perfect gas law at some combinations of temperature and pressure, the extent depending on the gas. This behavior is described by a dimensionless compressibility factor Z that corrects the perfect gas law for real-gas behavior, FV = ZRT. Any consistent units may be used. Z is unity for an ideal gas, but for a real gas, Z has values ranging from less than 1 to greater than 1, depending on temperature and pressure. The compressibihty faclor is described further in Secs. 2 and 4 of this handbook. 

The turboexpander in combination with a compressor and a heat exchanger functions as a heat pump and is analyzed as follows In Fig. 29-44 consider the compressor and aftercooler as an isothermal compressor operating at To with an efficiency and assume the working fluid to be a perfect gas. Further, consider the removal of a quantity of heat by the tumoexpander at an average low temperature Ti-This requires that it dehver shaft work equal to Q. Now, make the reasonable assumption that one-tenth of the temperature drop in the expander is used for the temperature difference in the heat exchanger. If the expander efficiency is and this efficiency is mul-... 

Ideal gas obeys the equation of state PV = MRT or P/p = MRT, where P denotes the pressure, V the volume, p the density, M the mass, T the temperature of the gas, and R the gas constant per unit mass independent of pressure and temperature. In most cases the ideal gas laws are sufficient to describe the flow within 5% of actual conditions. When the perfect gas laws do not apply, the gas compressibility factor Z can be introduced ... 

This equation can be rewritten for a thermally and calorifically perfect gas in terms of total pressure and temperature as follows ... 

Charles and Gay-Lussac, working independently, found that gas pressure varied with the absolute temperature. If the volume was maintained constant, the pressure would vary in proportion to the absolute temperature [I j. Using a proportionality constant R, the relationships can be combined to form the equation of state for a perfect gas, otherwi.se known as the perfect gas law. 

The specific gravity, SG, is the ratio of the density of a given gas to the density of dry air at the same temperature and pressure. It can be calculated from the ratio of molecular weights if the given gas is a perfect gas. 

About 1902, J. W. Gibbs (1839-1903) introduced statistical mechanics with which he demonstrated how average values of the properties of a system could be predicted from an analysis of the most probable values of these properties found from a large number of identical systems (called an ensemble). Again, in the statistical mechanical interpretation of thermodynamics, the key parameter is identified with a temperature, which can be directly linked to the thermodynamic temperature, with the temperature of Maxwell s distribution, and with the perfect gas law. 

The volumetric flowrate depends on the temperature and changes as the temperature changes. Assuming a perfect gas behavior. 

Absolute zero The temperature at which a perfect gas kept at constant volume exerts no pressure it is equal to -273.16 °C (0 K). 

Whereas Fishbum was mainly interested in the detonative mode of explosion, Luckritz (1977) and Strehlow et al. (1979) focused on the simulation of generation and decay of blast from deflagrative gas explosions. For this purpose, they employed a similar code provided with a comparable heat-addition routine. Strehlow et al. (1979), however, realized that perfect-gas behavior, which is the basis in the numerical scheme for the solution of the gas-dynamic conservation equations, is an idealization which does not reflect realistic behavior in the large temperature range considered. 

This equation of state applies to all substances under all conditions of p, and T. All of the virial coefficients B, C,. .. are zero for a perfect gas. For other materials, the virial coefficients are finite and they give information about molecular interactions. The virial coefficients are temperature-dependent. Theoretical expressions for the virial coefficients can be found from the methods of statistical thermodynamic s. 

Figures 2-38A and 2-38B are based on the perfect gas laws and for sonic conditions at the outlet end of a pipe. For gases/vapors that deviate from these laws, such as steam, the same application will yield about 5% greater flow rate. For improved accuracy, use the charts in Figures 2-38A and 2-38B to determine the dowmstream pressure when sonic velocity occurs. Then use the fluid properties at this condition of pressure and temperature in ...

Compressibility is expressed as the multiplier for the perfect gas law to account for deviation from the ideal. At a given set of conditions of temperature and pressure ... 

Ideal (or perfect) gas behavior is approached by most vapors and gases in the limit of low pressures and elevated temperatures. Two special forms of restricted utility known as the Boyle s law and the Charles law preceded the development of the perfect gas law. 

The mole is particularly useful when working with gas mixtures. It is based on Avogdro s law that equal volumes of gases at given pressure and temperature (pT) conditions contain equal number of molecules. Since this is so, then the weight of these equal volumes will be proportional to their molecular weights. The volume of one mole at any desired condition can be found by the use of the perfect gas law. 

Review of Solutions in General. In the discussion of these various examples we have noticed at extreme dilution the prevalence of the term — In Xb, or alternatively — In yB. The origin of this common factor in many different types of solutions can be shown, as we might suspect, to be of a fundamental nature. For this purpose let us make the familiar comparison between a dilute solution and a gas. Since the nineteenth century it has been recognized that the behavior of any solute in extremely dilute solution is, in some ways, similar to that of a gas at low pressure. Now when a vessel of volume v contains n particles of a perfect gas at a lixed temperature, the value of the entropy depends on the number of particles per unit volume, n/v. In fact, when an additional number of particles is introduced into the vessel, the increment in the entropy, per particle added, is of the form... 

The satisfactory result shown in Table 12 suggests that one might give a more detailed and quantitative discussion of the variation with temperature. If we are to do this, we need some standard of comparison with which to compare the experimental results. Just as wq compare an imperfect gas with a perfect gas, and compare a non-ideal solution with an ideal solution, so we need a simple standard behavior with which to compare the observed behavior. We obtain this standard behavior if, supposing that. /e is almost entirely electrostatic in origin, we take J,np to vary with temperature as demanded by the macroscopic dielectric constant t of the medium 1 that is to say, we assume that Jen, as a function of temperature is inversely proportional to . For this standard electrostatic term we may use the notation, instead of... 

In Section 6.3 we saw how to calculate the work of reversible, isothermal expansion of a perfect gas. Now suppose that the reversible expansion is nor isothermal and that the temperature decreases during expansion, (a) Derive an expression for the work when T = Tinitja — c( V — Vjnitia ), with c a positive constant, (b) Is the work in this case greater or smaller than that of isothermal expansion Explain your observation. 

FIGURE 7.4 The c hange in entropy as a sample of perfect gas expands at constant temperature. Here we have plotted IS/nR. The entropy increases logarithmically with volume. 

M is the molar mass and Vm the molar volume expressed in litres, which, if compared with the vapour produced by a perfect gas, gives, depending on the temperature at which Cgq is measured ... 

Volatility is the weight of vapor present in a unit volume of air, under equilibrium conditions, at a specified temperature. It is a measure of how much material (agent) evaporates under given conditions. The volatility depends on vapor pressure. It varies directly with temperature. We express volatility as milligrams of vapor per cubic meter (mg/m3). Calculate it numerically by an equation derived from the perfect gas law. This equation follows ... 

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