Reversible vs. irreversible processes

Transcription

1 Reversible vs. irreversible processes A reversible process is one for which the final states of the universe (system and environment) are iden<cal to the ini<al states. Consider, for example, a parcel ascending adiaba<cally and reversibly. As it rises, it expands (it does work on the environment), which by the 1 st Law requires its internal energy (and thus temperature) to decrease. As it descends, it is compressed (the environment does work on the parcel), which by the 1 st Law requires its internal energy (and thus temperature) to increase. An irreversible process is one in which the ini<al and final states are dis<nct. Note that a process in which the system has iden<cal ini<al and final states is irreversible if the environment is permanently altered. We will see later that this is an informal way of sta<ng the 2 nd Law of Thermodynamics. A popping balloon is irreversible. In prac<ce, no real- world process is strictly reversible. On the other hand, a process can be approximated as reversible if it is always in a state close to equilibrium. This effec<vely requires the process to occur more slowly than the rate at which the system equilibrates.

2 Enthalpy (or specific enthalpy) The enthalpy (extensive, H) or specific enthalpy (intensive, h) is, like the internal energy, a measure of the energy of a system. Specific enthalpy is given by: h = u + p! We can interpret the 2 nd term as the energy necessary (analogous to work) required for a given parcel of air at pressure p to displace a volume per unit mass of the environment (the atmosphere). If we add an increment of heat δq to a parcel at constant pressure, it gains an increment of enthalpy dh equal to δq. dh accounts for both the change in internal energy as well as the mechanical work that would be required to displace the atmosphere. p!

3 Aside: Thermodynamic Poten<als In physics, we define a poten2al as generalized force F i <mes displacement d i : " = F i d i In thermodynamics, quan<<es like internal energy and enthalpy (among others), are known as thermodynamic poten2als. Such quan<<es are related in fundamental ways; these rela<onships can be exploited in many useful ways. Internal energy (U): U = U(S,V, { N i }) = TS " PV + µ i N i Helmholtz free energy (A): A = A(T,V, { N i }) = U " TS Gibbs free energy (G): G = G(T,P, { N i }) = U " TS + PV Enthalpy (H): H = H(S,P, { N i }) = U + PV Landau or Grand Poten2al (Ω): " = "(T,V,{ µ i }) = U # TS # µ i N i Chemical poten/al (µ i ): force related to par/cle exchange (of species i) between systems Euler s homogeneous func/on theorem allows U to be wriuen in terms of TS, PV, Legendre transforms can be applied to relate one poten<al to another. Different poten<als are useful for different applica<ons, e.g., Gibbs is useful for processes in T- P space. Maxwell rela/ons are equivalences of mixed 2 nd par<al deriva<ves. We won t use these in this class, but you may see them used in other courses.

4 Enthalpy conserva<on Consider a parcel moving adiaba<cally (and reversibly). From the 1 st Law: From the defini<on of specific enthalpy: So:!q = du + pd" dh = d(u + p!) = du + pd! +!dp!q = 0 = dh!"dp = dh!"(#gdz) = d(h +$) where we have invoked the adiba<c condi<on (δq = 0), hydrosta<c balance, and the defini<on of geopoten<al. We thus conclude that the quan<ty h+ϕ is conserved for adiaba<c, reversible mo<on. This quan<ty is referred to as dry sta2c energy (s d ).

5 Dry sta<c energy and an irreversible process Consider a parcel at temperature T and the environment at temperature T. In this case, the parcel is not in equilibrium with the environment. Suppose T > T, in which case ρ < ρ, then: (1) The parcel is posi<vely buoyant with respect to the environment; (2) Posi<ve buoyancy represents a net upward force (per mass) ac<ng on the parcel, so it accelerates upward, and in turn gains kine<c energy (per mass), e k ; (3) Once the parcel has reached a speed for which it gains e k at the same rate as it dissipates e k through fric<on, its speed becomes constant, so de k = 0; (4) The fric<onal dissipa<on of e k manifests in the form of heat, which may be transferred to both the parcel and environment. If the process were adiaba<c and fric<onless, h+ϕ+e k would be constant. However, for a nonadiba<c (and thus, irreversible process), since we do not know a priori how the hea<ng is par<<oned between the parcel and its environment, all we can determine is that:!q > d(h +")

6 Annotated Skew-T skew- t.com

7 Subsidence inversion For a subsidence inversion, a layer of air of fixed mass descends adiba<cally. Because the process is adiba<c, the air within the layer remains on a given adiabat (line of constant ϑ). Thus in the diagram, the air ini<ally at the top of the layer (100 mb) remains on the 313K adiabat throughout descent, while the air at the bouom of the layer (200 mb) remains on the 293K adiabat. Since mass is conserved, the pressure difference between the top and bouom of the layer is constant (in this case, 100 mb). PeUy Figure 5.5