Processes at constant pressure

But another approach to multi-step cooling [8, 9] involves dealing with the turbine expansion in a manner similar to that of analysing a polytropic expansion. Fig. 4.4 shows gas flow (1 + ijj) at (p,T) entering an elementary process made up of a mixing process at constant pressure p, in which the specific temperature drops from temperature T to temperature T, followed by an isentropic expansion in which the pressure changes to (p dp) and the temperature changes from T to (7 - - dT). 

Consider a process at constant pressure for which the change in internal energy is AU and the change in volume is A V. It then follows from the definition of enthalpy in Eq. 9 that the change in enthalpy is... 

Because of this expansion work, a process at constant pressure involves both heat and work ... 

The heat absorbed in a process at constant pressure is equal to AH, the increase in the enthalpy of the system. It can thus be said that the heat change accompanying a chemical reaction is equal to the difference between the total heat content of the products and that of the reactants, at constant pressure and temperature conditions. This quantity is called the heat of reaction, AH, and can be expressed as follows... 

From Equation (3.13), show that DQ is an exact differential for a process at constant pressure in which only PV work is performed. 

Let us start by considering the quantity of heat DQp that is exchanged in a process at constant pressure when only PV work is performed. From the first law,... 

An increase in enthalpy therefore denotes the heat absorbed during a process at constant pressure. For the case of constant volume the process is simpler as the system does no work on its surroundings, i.e., pAv = 0. Therefore,... 

It is common to equate the strength of interaction of an acid and a base with the enthalpy of reaction. In some cases this enthalpy may be measured by direct calorimetry AH q for an adiabatic process at constant pressure. 

Processes at constant pressure. Chemical and biochemical reactions are much more likely to be conducted at constant pressure (usually 1 atm) than they are at constant volume. For this reason, chemists tend to use the enthalpy H more often than the internal energy E. 

It follows from Eq. 6-3 that if the pressure is constant, AHp is equal to AEP + P AV. Since in a process at constant pressure, P AV is exactly the pressure-volume work done on the surroundings, the heat absorbed at constant pressure (Qp) is a measure of AHp. 

For a process at constant pressure (AP = 0), in which the only work performed is the mechanical pressure-volume work (PAV). the change in enthalpy, A H. is equal to the heat adsorbed by the system, tf (hence the name heat content) ... 

Enthalpy-Temperature Relation and Heat Capacity When heal is adsorbed by a substance, under conditions such that no chemical reaction or slate transition occur and only pressure-volume work is done, the temperature. T, rises and the ratio of the heat adsorbed, over the differential temperature increase, is by definition the heat capacity. For a process at constant pressure (following Equation (2)). this ratio is equal to the partial derivative of the enthalpy, and it is called the hear capacity at constant pressure. C,. (usually in calories/degree-mole) ... 

The total entropy change, AStot, is the sum of the changes in the system, AS, and its surroundings, ASsurr, with AStot = AS + ASsurr. For a process at constant pressure and temperature, the change in the entropy of the surroundings is given by Eq. 11, ASvllrr = —AH/T. Therefore, under these conditions,... 

The mass transport in electromembrane processes at constant pressure and temperature can be described as a function of the driving force by a phenomenological equation [17], that is, ... 

Josiah Willard Gibbs studied thermodynamics and statistical mechanics in the 1870s. He formulated the concept now called Gibbs free energy that will determine whether or not a chemical process at constant pressure will spontaneously occur. 

For an adiabatic combustion process at constant pressure, the enthalpy stays constant. Figure 2 shows the exergy of the reactants, e, and the exergy of the reaction products, e , after this reaction has taken place. The loss in exergy is ... 

Standard thermodynamic operations (Prigogine and Defay, 1954) on the Gibbs function, AG, yield expressions for related thermodynamic activation parameters. Thus the dependence of k on T can be used to calculate the enthalpy of activation, A, for processes at constant pressure or the thermodynamic energy of activation, A, for processes at constant volume, which in turn lead to the related entropies of activation, ASp and AS respectively. The dependence of k on pressure can be used to calculate the volume of activation, AV which is related to AHp by eqn (5) where a is the thermal... 

The equation of state-does not include all the experimental information which we must have about a system or substance. Ve need to tnow also its heat, capacity or specific heat, as a function of temperature. Suppose, for instance, that we know the specific heat at constant pressure Cp as a function of temperature at a particular pressure. Then we can find the difference of internal energy, or of entropy, between any two states. From the first state, we can go adiabatically to the pressure at which we know Cp, In this process, since no heat is absorbed, the change of internal energy equals the work done, which we can compute from the equation of state. Then we absorb heat at constant pressure, until we reach the point from which another adiabatic process will carry us to the desired end point. The change of internal energy can be found for the process at constant pressure, since there we know CP) from which we can... 

The volume change accompanying the charging process at constant pressure is negligible, and so W -- Wo may be identified with the difference between the electrical free energy of an ionic solution at a definite concentration and at infinite dilution. 

Consider now what happens if the liquid is a mixture of several components. As heat is added, the liquid temperature rises until a temperature is reached at which the first bubble of vapor forms. Up to this point, the process looks like that for a single component. However, if the liquid is a mixture, the vapor generated generally will have a composition different from that of the liquid. As vaporization proceeds, the composition of the remaining liquid continuously changes, and hence so does its vaporization temperature. A similar phenomenon occurs if a mixture of vapors is subjected to a condensation process at constant pressure at some temperature the first droplet of liquid forms, and thereafter the composition of the vapor and the condensation temperature both change. 

Saturated steam at 100°C is healed to 400 C. Use the steam tables to determine (a) the required heal input (J/s) if a continuous stream flowing at 100 kg/s undergoes the process at constant pressure and (b) the required heat input (J) if 100 kg undergoes the process in a constant-volume... 

Thus, as above, a rise in temperature raises the entropy of the system during a process at constant pressure and composition. Also, the heat capacity at constant pressure and composition cannot be negative. 

The free energy is derived from the entropy and is, in many ways, a more useful function to use. The free energy which is referred to when we are discussing processes at constant pressure is the Gibbs free energy (G). This is defined by... 

Because U, P, and V are state functions, H must also be a state function. Heat transfer in a process at constant pressure has therefore been related to the change in a state function. 

For processes at constant pressure P and constant temperature T (the usual case in electrochemical cells),... 

Gibbs free energy Energy liberated or absorbed in a reversible process at constant pressure and constant temperature. 

---