Reversible expansion work

Derive an explicit equation for the reversible work of an isothermal expansion for each of the following cases ... 

In any intermediate isothermal expansion, the work performed by the gas is not zero, but it is less in magnitude than that obtained by reversible means (see Table 5.1). As A / is zero and as... 

A hypothetical cycle for achieving reversible work, typically consisting of a sequence of operations (1) isothermal expansion of an ideal gas at a temperature T2 (2) adiabatic expansion from T2 to Ti (3) isothermal compression at temperature Ti and (4) adiabatic compression from Ti to T2. This cycle represents the action of an ideal heat engine, one exhibiting maximum thermal efficiency. Inferences drawn from thermodynamic consideration of Carnot cycles have advanced our understanding about the thermodynamics of chemical systems. See Carnot s Theorem Efficiency Thermodynamics... 

The second term is the reversible work done at a given stress by the volume expansion (contraction) Vdujk if one adds dn,- to the system under stress. For uniaxial stress, this is (q = cross section area = crystal length)... 

For the expansion of a perfect gas at constant temperature, the reversible work is given by the expression ... 

Reality is always more complicated than idealized models used by scientists and engineers. For example, the relationship W = P AV is valid only under reversible conditions, that is when AV is accomplished in an infinite number of steps and the pressure is held constant for all of the steps. That is, the expansion would take forever. Under these conditions this is known as reversible work. Obviously, we never obtain reversible work. However, the slower the change in volume, the closer the approximation. 

This means the following The change in free energy in a reaction is equal to the total reversible work obtainable from the reaction (this includes all kinds of work, i.e., gravitational, electrical, surface, etc., and also the work of expansion) diminished by the work of expansion, PAV. Hence,... 

The vapor pressure of water at 25 C is 23.76 mm. Calculate the reversible work of expansion in (i) liter-atm., (ii) defined cal., when the pressure of 100 g. of water vapor is decreased isothermally to 0.001 atm., assuming ideal behavior. 

Show that for a van der Waals gas, the isothermal, reversible work of expansion for 1 mole is given by... 

The quantity Wm, represents the total reversible work obtainable in the given change this may include other forms of work, e.g., electrical or surface work, in addition to work of expansion. The latter is equal to PAV ( 3g), and so Wrav. — PAV represents the reversible work, exclusive of work of expansion, that can be obtained from a given change in state. This quantity is sometimes referred to as the net work, and is represented by so that by equation (25.10),... 

H is the sum of (a) the internal energy U, and (b) the reversible work done on the system at a pressure of p as a result of the thermal expansion (change of the molar volume V) caused by the added thermal energy. 

The decrease of enthalphy is the measure of reversible work that can be extracted from a flowing fluid upon expansion. 

This is illustrated in Figure 4.4. The diagram to the left shows the reversible expansion of a gas in which the pressure is falling as the volume increases. The reversible work done by the system is given by the integral... 

The left-hand diagram a illustrates the reversible work of expansion from t/i to 1/2 (compare Figure 43). The right-hand diagram b shows the irreversible work that would be performed by the system if the external pressure were suddenly dropped to the final value Pi. 

The deviation ofthe work performed in areal expansion of a gas from that of reversible expansion can be shown to be of order dlKu). Here (u) is the average molecular speed and the is the speed of the piston. What piston speed is required f or a 10 % deviation from the reversible work formula ... 

On the other hand, when during the expansion no work is done, the gas remains isothermal. This process is addressed as the Gay - Lussac process. In general, we cannot state for an isothermal process, whether the process is reversible or not. 

The third term indicates the work associated with the expansion and compression of the fluid (a reversible work). 

The expansion of the gas illustrated in Figure 19.5 causes an increase in entropy. To illustrate how this entropy change can be calculated, we can employ Equation 19.1, which applies to the ejqjansion of an ideal gas. For an isothermal expansion, the reversible work is given b) ... 

This formula for reversible work of expansion requires calculus for its derivation. It is not necessary for you to remember it... 

The expression dw = —pdV for reversible expansion work of an isotropic phase is the product of a work coefficient, —p, and the infinitesimal change of a work coordinate, V. In the reversible Umit, in which all states along the path of the process are equihbrium states, the system has two independent variables, e.g., p and F or T and V. The number of independent variables is one greater than the number of work coordinates. This will turn out to be a general rule The number of independent variables needed to describe equilibrium states of a closed system is one greater than the number of independent work coordinates for reversible work. 

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