Chapter 1 Basic concepts of thermodynamics

1. Chapter 1Basic concepts of thermodynamics

2. thermo: concerned with the state of a systemwhen left , or when with the surroundings • system: separated from the by a real or imaginary wall • properties of determine the way of interaction • two kinds of interactions thermal + mechanical → thermodynamics exchange of matter → • a set of independent components: chemical components (c) plus thermal and mechanical → c+2 • metallic: components identical to elements • covalent: components as stable molecular species • ionic: components → neutral compounds rather than ions

3. state of equil • the state that can be established from starting points • state variables (상태변수) or state functions (상태함수) - for example: T, P, V and Ni (amount of each component) - a particular state of equil identified by giving the values to state variables  c+2 variables must be given  the rest are dependent - equil state of system : represented by a point in a c+2 dim diagram, all pts in such a diagram represent possible states  diagram (but, giving no information) - thus, by sectioning at constant values of c+1 variables and plotting a dependent variable as another axis diagram (Fig. 1.1) - the line itself represents the property of the system  property diagram

4. the content of matter in a system being kept constant and the wall only open for exchange of mechanical work and heat  such system is called a system - if changeable  an system, an alloy system in metallurgy - its behavior often shown in so-called phase diagram • two kinds of state variables: 1. 세기변수 (intensive): for example, T, P - they can be defined at each of the system - called if same value at all points at equil - some of them may have different values at different parts of the system → not a potential 2. 크기변수 (extensive): for example, V, U, Ni - its value being equal to the of its values of all parts of the system, obeying the law of additivity

5. system: 고립계 - when left completely alone - contained inside a wall (rigid, insulating and impermeable to matter) • externalvar (변수): - in an open system, open to all these changes of mech work, heat or matter - controlling the values of c+2 variables, thus regarded as external • var (변수): - they will change due to internal processes as the system approaches the state of new equil from old one - 내부적으로 중간 단계 有 (internal process) - ξ (ksi) by De Donder, 1922

6. Fig. 1.2 - ξ: no of vacancies per mole of the metal or C + Cr0.7C0.3 → Cr0.6C0.4 (the amount)

7. the 1st law of thermo - development of thermo started by defining Q and W - ΔU = Q + W: energy cannot be nor - dU = dQ + dW (in differential form) → U, state var - Q and W, not properties of the system → but defining different ways of interaction with - U: not easy to vary → state ft rather than state var - convenient to consider U=U(T,P) at equil - however, soon T, P are proved unnatural variables - U≡0 not defined, no natural zero point for U

8. reversible and irreversible in Carnot - heat can never flow from a cold reservoir to warmer - heat conduction is irreversible - 등온 (isothermal): 100% reversible? - 단열 (adiabatic): how come an irreversible character? - a completely reversible process is always an idealization of • freezing-in - exp cond when ξ (internal var) does not change - dξ = 0, frozen-in, but non equil state

9. the 2nd law of thermo: entropy by - no permanent engine - irrev: dipS(internal entropy production) > 0 - rev: dipS = 0, or dS = - • cond of internal equil (내부 평형 조건) - from the 2nd law, an internal process may continue as long as dipS 0 - internal process stopseventually at dipS ≤ 0, and internal equil reached

10. Fig. 1.4 Fig. 1.5

11. driving force (구동력) - internal var ξ: extent of an internal process - dipS, a function of ξ - dipS/dξ , a new state function - 편의상 T를 곱해서 D=T·dipS/dξ (D: 구동력, classical chemical affinity) • Ddξ = T·dipS - ξ: 반응 정도 extensive, D: conjugate, intensive - if a system not in equil, then a spontaneous process - dipS > 0 and Ddξ > 0 → therefore, D and dξ have the same sign - dξ is given a positive value in the direction one wants to examine (+) - D > 0 (rate of process predicted from magnitude of D) - D = 0, ξ≠ 0 at equil - D > 0 if not in equil

12. combined 1st & 2nd law dS = dQ/T + dipS from the 2nd law ∴ TdS = dQ + TdipS = dQ + Ddξ ∴ Ddξ = TdS - dQ ≥ 0 ∴ dQ ≤ TdS (this form frequently shown in textbooks) • dU = dQ - PdV = TdS - Ddξ – PdV from the 1st law → TdS = dU + PdV + Ddξ ( S is maximized at const U and V ) according to entropy scheme, dS = → S: a state function, U & V are natural variables for S →U & V completely controlled by actions from the external world (external state variable) whereas ξ is an internal state variable

13. more common form: dU = TdS - PdV - Ddξ ( scheme) • S is regarded as external although influenced by internal process, not 100% external var • dU ≡ intensive * d(extensive) - Ddξ = ∑Ya *dXa - Ddξ - Ya and Xa are conjugate var, at the same time they are external var - why -P rather than +P? to be comparable with other potentials • general cond of equil - a system in a state of equil if the for all possible internal processes is zero, D = 0

14. dU = ∑Ya *dXa - Ddξ D = ∴ dU = 0 at equil (for const Xa) • the process can occur spontaneously until U reached a min, U is minimized because - Ddξ < 0 ∴ the state of min U is equil at const S & V • a transfer of dXb from sub’ (one half of the system) to sub” (the other half), measuring the extent of this internal process by identifying dξ = -dXb = -Yb’ + Yb”

15. ∴ D = Yb’– Yb” - what is its meaning? - the driving force for this process is zero and the system in equil if the potential Yb has the same value in two parts of the system (Yb’ = Yb”) - this has proved that each potential must have the value in the whole system at equil - applicable to T, P and i

16. characteristic state function - combination of 1st and 2nd laws allowing us to calculate how U changes as a result of variation in S and V - not very easy to control S & V, but relatively easy to control T & P (from an experimental point of view) - desirable to change indep var - dU = TdS - PdV - Ddξ → U - TS + PV - d(U - TS + PV) = dU - TdS - SdT + PdV + VdP = -SdT + VdP - Ddξ

17. this transform → changing natural var of U → different natural variables • G = G(T, P, ξ), U = U(S, V, ξ) - eq. of state: Legendre transformation - why fundamental? if we know S and V representing U, then - also G = U –TS + PV can be obtained = G(S, V, ξ) but this is not fundamental (caloric eq of state) - S or V cannot be obtained from G(S, V, ξ)

18. Legendre transform U = U(S, V, ξ) → U = U(T, P, ξ) • how come? - replacing Xa(extensive) with Ya(intensive) • what is Ya ? - slope of U vs Xa (potential) - any line or curve form of U → all the information pertaining to this line or curve form transferred to a new energy function by using slope and intercept

19. U U

20. ψis called a Legendre transform of U → creating F, H, G → Legendre transforms of U • important property of ψ the negative sign is very meaningful !

21. general conditions of equilibrium (at equil)