Energy of ideal gas

The average kinetic energy of ideal gas particles is directly proportional to the Kelvin (K) temperature of the gas. 

Figure 10.1 Gibbs energy of ideal gas as a function of pressure.

Using expression c (T) = de/dT, one can find the change of internal energy of ideal gas with change of its temperature from To to T ... 

The explanation is that the internal energy of ideal gas solely has the form of molecular kinetic energy Ek, the potential energy of the gas is zero because no forces act between gas particles of ideal gas. At the same time, this also makes it clear that fulfilment of such ideal state can only be approximate in real gases. 

We used the relation in Equation 11.53 in Chapter 1 to find fhe average energy of ideal gas particles. These particles are noninteracting (part of the idealization), though they can exchange kinetic energy via instantaneous collisions. This means that for an ideal gas, the ensemble partition function is a product of q s, with a factor to accoimt for indistinguishability. 

Figure 7.4 Gibbs energy of ideal gas species a and b. Curve 1 plots the value of g for a given composition for the two gases that are separated, while curve 2 plots the lowering of g when a and b mix, due to the Gibbs energy of mixing.

Heat Capacity, C° Heat capacity is defined as the amount of energy required to change the temperature of a unit mass or mole one degree typical units are J/kg-K or J/kmol-K. There are many sources of ideal gas heat capacities in the hterature e.g., Daubert et al.,"" Daubert and Danner,JANAF thermochemical tables,TRC thermodynamic tables,and Stull et al. If C" values are not in the preceding sources, there are several estimation techniques that require only the molecular structure. The methods of Thinh et al. and Benson et al. " are the most accurate but are also somewhat complicated to use. The equation of Harrison and Seaton " for C" between 300 and 1500 K is almost as accurate and easy to use ... 

Gibbs free energy of formation of ideal gas (AGf, kjoule/g-mol) is calculated from the tabulated coefficients (A, B, C) and the temperature (T, °K) using the following equation ... 

The pressure vessel under consideration in this subsection is spherical and is located far from surfaces that might reflect the shock wave. Furthermore, it is assumed that the vessel will fracture into many massless fragments, that the energy required to mpture the vessel is negligible, and that the gas inside the vessel behaves as an ideal gas. The first consequence of these assumptions is that the blast wave is perfectly spherical, thus permitting the use of one-dimensional calculations. Second, all energy stored in the compressed gas is available to drive the blast wave. Certain equations can then be derived in combination with the assumption of ideal gas behavior. 

The adiabatic expansion of a gas is an example of (b). In the reversible adiabatic expansion of one mole of an ideal monatomic gas, initially at 298.15 K, from a volume of 25 dm3 to a final volume of 50 dm3, 2343 J of energy are added into the surroundings from the work done in the expansion. Since no heat can be exchanged (in an adiabatic process, q = 0), the internal energy of the gas must decrease by 2343 J. As a result, the temperature of the gas falls to 188 K. 

Debye heat capacity equation 572-80 Einstein heat capacity equation 569-72 heat capacity from low-lying electronic levels 580-5 Schottky effect 580-5 statistical weight factors in energy levels of ideal gas molecule 513 Stirling s approximation 514, 615-16 Streett, W. B. 412... 

The kinetic model of gases is consistent with the ideal gas law and provides an expression for the root mean square speed of the molecules vnns = (3RT/M)l/2. The molar kinetic energy of a gas is proportional to the temperature. 

Calculate the fraction of ideal-gas molecules with translational kinetic energy equal to or greater than 5000 J mol-1 (a) at 300 K, and (b) at 1000 K. 

Ref 22, pp 161-62. Under the title "Thermal Effect of Impact is discussed initiation of liquid expls, such as NG, NGc, etc. It differs from initiation of solid expls (discussed on p 153 of Ref 22) in that there is no friction between crystals as in solids, but everything depends on rise of temperature created by adiabatic compression of gas or vapor in minute bubbles.. For example, with NG contg a bubble as small as 0.1 mm in diam 100% explns can be obtd with impact energy of 400 gram-cm, while 10 to 10 g-cm are required when no gas bubble is present. The temp T2 reached in a bubble due to adiabaric compression of the gas depends, in the case of ideal gas, on the... 

Kinetic energy is the energy of motion. Gas particles have a lot of kinetic energy and constantly zip about, colliding with one another or with other objects. The picture is complicated, but scientists simplified things by making several assumptions about the behavior of gas pcirticles. These assumptions are called the postulates of the kinetic molecular theory. They apply to a theoretical ideal gas ... 

In effect, activity a is a way of encoding Gibbs free energy of real gases in equations that appear to be of ideal gas form ... 

Consequently, the energy of the gas is constant for the isothermal reversible expansion or compression and, according to the first law of thermodynamics, the work done on the gas must therefore be equal but opposite in sign to the heat absorbed by the gas from the surroundings. For a reversible process the pressure must be the pressure of the gas itself. Therefore, we have for the isothermal reversible expansion of n moles of an ideal gas between the volumes F and V... 

It is informative, however, to consider the dependence of this function on the temperature. Since we know it is characteristic of the pure gas, we consider only 1 mole of a pure gas. Moreover, we limit the discussion to an ideal gas. There are two possible methods, one concerning the energy and entropy and the other the enthalpy and entropy, but we use only the energy and entropy here. The differential of the energy of 1 mole of ideal gas is dE = v dT. On... 

There is no change in (internal) energy of the gas as its volume is increased (i.e. gas is expanded) whilst the temperature is kept constant. This provides a convenient mathematical definition (in thermodynamic terms) of an ideal gas. 

As shown in Chap. 6, ideal-gas heat capacities, rather than the actual heat capacities of gases, are used in the evaluation of thermodynamic properties such as internal energy and enthalpy. The reason is that thermodynamic-property evaluation is conveniently accomplished in two steps first, calculation of ideal-gas values from ideal-gas heat capacities second, calculation from PVT data of the differences between real-gas and ideal-gas values. A real gas becomes ideal in the limit as P - 0 if it were to remain ideal when compressed to a finite pressure, its state would remain that of an ideal-gas. Gases in these hypothetical ideal-gas states have properties that reflect their individuality just as do real gases. Ideal-gas heat capacities (designated by Cf and Cy) are therefore different for different gases although functions of temperature, they are independent of pressure. 

Example 7.1 Consider the filling of an evacuated tank with a gas from a cons, pressure line. What is the relation between the enthalpy of the gas in the entras line and the internal energy of the gas in the tank Neglect heat transfer between 1 gas and the tank. If the gas is ideal and has constant heat capacities, how is ti temperature of the gas in the tank related to the temperature in the entrance line ... 

This result shows that in the absence of heat transfer the energy of the gas contained within the tank at the end of the process is equal to the enthalpy of the gas added. If the gas is ideal,... 

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