Adiabatic expansion 765

When a real gas like hydrogen expands freely, its temperature may either decrease or increase, depending on the initial temperature and pressure. The change of 

---

One assumes the existence of a fluid that obeys Boyle s law (equation (A2.1.4) ) and that, on adiabatic expansion into a vacuum, shows no change in temperature, i.e. for which/yF=/(0) and = 0. (All... 

The air spring effect results from adiabatic expansion and compression of the air in the actuator casing, Niirnericallv, the small perturbation value for air spring stiffness in Newtons/rneter is given bv Eq, (8-107),... 

The Carnot refrigeratiou cycle is reversible and consists of adiabatic (iseutropic due to reversible character) compression (1-2), isothermal rejection of heat (2-3), adiabatic expansion (3-4) and isothermal addition of heat (4-1). The temperature-entropy diagram is shown in Fig. 11-70. The Carnot cycle is an unattainable ideal which serves as a standard of comparison and it provides a convenient guide to the temperatures that should be maintained to achieve maximum effectiveness. 

These mechanisms can be observed in many common situations. For example, fog via mixing can be seen in the discharge of breath on a cold day. Fog via adiabatic expansion can be seen in the low-pressure area over the wing of an airplane landing on a humid summer day and fog via condensation can be seen in the exhaust from an automobile air conditioner (if you follow closely enough behind another car to pick up the ions or NO molecules needed for nucleation). All of these occur at a veiy low supersaturation and appear to be keyed to an abundance of foreign nuclei. All of these fogs also quickly dissipate as heat or unsaturated gas is added. 

Steam Rate Enthalpy data can be obtained from Mollier diagrams or from steam tables (see Sec. 2), from which the theoretical steam rate can be calculated. For example, a throttle inlet condition of 4137 kPa (600 psig) and 399° C (750° F) gives an enthalpy of 3.2 MJ/kg (1380 Btu/lb), and if the end point is at 348 kPa (50 psig), then adiabatic expansion is to 2.69 MJ/kg (1157 Btu/lb). This gives 0.52 MJ/kg (223 Btu/lb) available, and the theoretical steam rate is calculated from the Btu equivalent per Idlowatthour or horsepower-hour ... 

The adiabatic expansion and compression serve only to change the temperature of tire gas widrout heat being absorbed or evolved, i.e. iso-entropic changes. The heat changes are therefore only related to the work which is done during the isothermal stages, which is given by... 

It follows that the efficiency of the Carnot engine is entirely determined by the temperatures of the two isothermal processes. The Otto cycle, being a real process, does not have ideal isothermal or adiabatic expansion and contraction of the gas phase due to the finite thermal losses of the combustion chamber and resistance to the movement of the piston, and because the product gases are not at tlrermodynamic equilibrium. Furthermore the heat of combustion is mainly evolved during a short time, after the gas has been compressed by the piston. This gives rise to an additional increase in temperature which is not accompanied by a large change in volume due to the constraint applied by tire piston. The efficiency, QE, expressed as a function of the compression ratio (r) can only be assumed therefore to be an approximation to the ideal gas Carnot cycle. 

To calculate the heat duty it must be remembered that the pressure drop through the choke is instantaneous. That is, no heat is absorbed or lost, but there is a temperature change. This is an adiabatic expansion of the gas w ith no change in enthalpy. Flow through the coils is a constant pressure process, except for the small amount of pressure drop due to friction. Thus, the change in enthalpy of the gas is equal to the heat absorbed. 

This equation is well known and often used to calculate initial fragment velocity, but its application can result in gross overestimation. Assuming adiabatic expansion of the ideal gas, it can be derived that ... 

Adiabatic expansion of the air in the engine causes a maximum temperature drop of the exhaust. Adiabatic compression causes a maximum temperature rise of the compressed air. These effects combine to cause the greatest work loss of any compressed-air system, when pressurized air must be cooled back to atmospheric temperature. The energy analysis parallels the one just made for the polytropic system. This shows that net areas on both PV and TS graphs measure the work lost. 

The fall of temperature per unit increase of volume in adiabatic expansion is equal to the increase of pressure per mechanical unit of heat supplied at constant volume, multiplied by the absolute temperature. 

On adiabatic expansion of liquid and vapour, show that (if a practically constant) ... 

The process occurring when steam is expanded by conversion to work without external heat loss or gain. Steam expanding behind the piston of a steam engine after the cutoff point approaches adiabatic expansion. 

An adiabatic expansion of the fluid is made from V2 to a volume V-. Work is done by the system, and the temperature drops to a lower empirical temperature 9, since no heat is added to the system. 

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. 

In an adiabatic expansion or compression, the system is thermally isolated from the surroundings so that q = 0. If the change is reversible, we can derive a general relationship between p, V, and T, that can then be applied to a fluid (such as an ideal gas) by knowing the equation of state relating p, V, and T. 

Example 3.8 Show that for the reversible adiabatic expansion of ideal gas with constant heat capacity... 

Solution In a reversible adiabatic expansion, 6qrev = T dS = 0. Thus, the process is isentropic, or one of constant entropy. To obtain an equation relating p, V and T, we start with... 

Figure 3.2 compares a series of reversible isothermal expansions for the ideal gas starting at different initial conditions. Note that the isotherms are parallel. They cannot intersect since this would give the gas the same pressure and volume at two different temperatures. Figure 3.3 shows a similar comparison for a series of reversible adiabatic expansions. Like the isotherms, the adiabats cannot intersect. To do so would violate the Caratheodory principle and the Second Law of Thermodynamics, since the gas would have two different entropies at the same temperature, pressure, and volume. 

---