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thermodynamics propeties

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2. 2. Thermodynamic -1
3. 3. Property relation for homogeneous phase According of first law for a close system for n moles ------1 We also know that together these three equation
4. 4. Conti………. U,S and V are molar valves of internal energy ,entroply and valume. Combing effect of both laws 1ST and 2nd Derived for reversible reaction But contain the property of the state of the system not process of the system Constant mass that result of differenital change from one equiriblrium state to another. Nature of the system cannot be relaxed
5. 5. Conti………. We know that H = U +PV GIBBS energy and Helmholtz energy equation A = U- TS----2 G= H-TS ----3 Putting the values on above equation so this equation becomes
6. 6. Conti………. When d(nU) replace by equation no 1 equation becomes 4 Same way multiplying equation 2 and 3 by n and takind differtional equations becomes 5 and 6
7. 7. Conti………. Equation 5 and 6 are subject of resection of equation 1. for the case of one mole of homogeneous fluid at constant pressure These are fundamental equations for homogeneous equaions
8. 8. Another set of equations follow from equation 6 and 7 for exactness for a differtional expression for a function f(x.y)
9. 9. Conti………. As result we get new sets of equations
10. 10. Entropy: Is a measure of disorder or randomness of a system. An ordered system has low entropy. A disordered system has high entropy. Enthalpy: Is defined as the sum of internal energy of a system and the product of the pressure and volume of the system. The change in enthalpy is the sum of the change in the internal energy and the work done. Enthalpy and entropy are different quantities. Enthalpy has the units of heat, joules. Entropy has the units of heat divided by temperature, joules per kelvin
11. 11. Enthalpy Vs. Entropy Enthalpy: It is donated by 'H', refers to the measure of total heat content in a thermodynamic system under constant pressure. Enthalpy is calculated ∆H = ∆E + P∆V (where E is the internal energy). The SI unit of enthalpy is joules (J). Entropy: It is denoted by 'S', refers to the measure of the level of disorder in a thermodynamic system. Entropy is calculated ∆S = ∆Q/T (where Q is the heat content and T is the temperature). It is measured as joules per kelvin (J/K).
12. 12. Relationship between Enthalpy and Entropy of a Closed System (T.∆S=∆H) Here, T is the absolute temperature, ∆H is the change in enthalpy, and ∆S is the change in entropy. According to this equation, an increase in the enthalpy of a system causes an increase in its entropy.
13. 13. Entropy pathleirreversibforS pathcyclicreversiblefor T dq S 0 0   
14. 14. How does entropy change with pressure? The entropy of a system decreases with an increase in pressure. Entropy is a measure of how much the energy of atoms and molecules become more spread out in a process. If we increase the pressure on the system, the volume decreases. The energies of the particles are in a smaller space, so they are less spread out. The entropy decreases. If we decrease the pressure on the system, the volume increases. The energies of the particles are in a bigger space, so they are more spread out. The entropy increases.
15. 15. Pressure Dependence of Entropy For solids and liquids entropy change with respect to pressure is negligible on an isothermal path. This is because the work done by the surroundings on liquids and solids is miniscule owing to very small change in volume. For ideal gas we can readily calculate the entropy dependence on the pressure as follows             1 2 ln . 0)( 0 . P P nRS P dP nR T dPV dS dP P V dVVdPPdVPVd E T dVP T dw T dq dS rev 
16. 16. Temperature dependence of Entropy Using the usual conditions such as isobaric or isochoric paths we can see that: Just as in case of ΔH the above formulae apply as long as system remains in single phase. On the other hand if system undergoes a phase transition, at constant temperature and pressure. pathisobaric T T C T dT C T dTC T dq S pathisochroic T T C T dT C T dTC T dq S PP P vv v                             1 2 1 2 ln ln
17. 17. Enthalpy & Entropy as function of Temp & pressure The most useful property relation for the Enthalpy and Entropy of a homogenous phase result when these properties expressed as function of T & P We need to know how H & S vary with Temperature and Pressure. Consider First the Temperature derivative. Equation 2.2 divide the heat capacity at constant pressure. PT H         PT S         TP H         TP S         P P C T H        
18. 18. Another Expression for this quantity is obtained by division of Eq. (6.8) by dT and restriction of the result to Constant P. Combination of this equation with Eq (2.2) gives The pressure derivative of the entropy results directly from Eq. (6.16) The Corresponding derivative for the enthalpy is found by division of Eq. (6.8) by dP and restriction to constant T. PP T S T T H                 T C T S P P         PT T V P S                
19. 19. As a Result of Equation (6.18) this become The functional relation chosen here for H & S are H = H(T , P) S = S(T , P) V P S T P H TT                 dP P H dT T H dH TP                  dP P S dT T S dS TP                  PT T V TV P H                
20. 20. The partial derivative are given by Eqs. (2.20) and (6.17) through (6.19) These are general Equation relating the Enthalpy and Entropy of homogenous fluid at constant composition to Temperature and pressure. dP T V TVdTCdH P P                dP T V T dT CdS P P         
21. 21. Internal energy as a function of P
22. 22. Internal energy is given as U = H – PV Differentiation yields As we know Now by putting this equation in above equation
23. 23. The ideal gas state As we know ideal gas By differentiating with respect to T and keeping P constant Now substituting this equation into following equations
24. 24. We got following equations Alternative forms for Liquids in following equations We got following
25. 25. Following when In following equation We obtain
26. 26. Internal energy and entropy as a function of T & P As we know dQ= 𝑇𝑑(𝑆)……………….1 dU= 𝑑𝑄 + 𝑑𝑊 … … … .2 Putting the of aqua 1 into aqua 2 dU= 𝑇𝑑 𝑆 − 𝑃𝑑(𝑉)….3 Temperature and volume often serve as more convenient independent variables hen do temperature pressure. The most useful relation are hen for infernal energy and entropy. Required derivatives are ( 𝜕𝑈 𝜕𝑇 )v ,( 𝜕𝑈 𝜕𝑉 )t ,( 𝜕𝑆 𝜕𝑇 )v ,( 𝜕𝑆 𝜕𝑉 )t
27. 27. taking he derivative of aqua 2 wish respect to temperature and volume at constant volume and temperature. ( 𝜕𝑈 𝜕𝑇 )v =T( 𝜕𝑆 𝜕𝑇 )v………………………….4 Cv= T( 𝜕𝑆 𝜕𝑇 )v CV/T=( 𝜕𝑆 𝜕𝑇 )v ( 𝜕𝑈 𝜕𝑉 )t =T( 𝜕𝑆 𝜕𝑇 )t-P………………….……5 ( 𝜕𝑈 𝜕𝑉 )t =T( 𝜕𝑆 𝜕𝑇 )t-P
28. 28. the chosen function here are U=U(T,V) S=S(T,V) taking derivative dU= ( 𝜕𝑈 𝜕𝑇 )v dT+ ( 𝜕𝑈 𝜕𝑉 )t dV………….6 dS=( 𝜕𝑆 𝜕𝑇 )v dT+ ( 𝜕𝑆 𝜕𝑉 )t dV…………….7 let
29. 29. dU= ( 𝜕𝑈 𝜕𝑇 )v dT+ ( 𝜕𝑈 𝜕𝑉 )t dV dU= Cv dT+[T ( 𝜕𝑆 𝜕𝑉 )-P]dV dS=( 𝜕𝑆 𝜕𝑇 )v dT+ ( 𝜕𝑆 𝜕𝑉 )t dV dS= CV/TdT+ ( 𝜕𝑃 𝜕𝑇 )vdV As we know ( 𝜕𝑃 𝜕𝑇 )v= 𝛃 𝚔
30. 30. It is applied to a state a constant volume Alternate form
31. 31. Gibbs free energy The energy associated with a chemical reaction that can be used to do work. The free energy of a system is the sum of its enthalpy (H) plus the product of the temperature (Kelvin) and the entropy (S) of the system:
32. 32. According to the second law of thermodynamics, for systems reacting at STP (or any other fixed temperature and pressure), there is a general natural tendency to achieve a minimum of the Gibbs free energy
33. 33. The Gibbs free energy is: which is the same as:
34. 34. where: U is the internal energy (SI unit: joule) p is pressure (SI unit: pascal) V is volume (SI unit: m3) T is the temperature (SI unit: kelvin) S is the entropy (SI unit: joule per kelvin) H is the enthalpy (SI unit: joule)
35. 35. Derivation The Gibbs free energy total differential natural variables may be derived via Legendre transforms of the internal energy. Where, μi is the chemical potential of the ith chemical component. (SI unit: joules per particle or joules per mole Ni is the number of particles (or number of moles) composing the ith chemical component
36. 36. The definition of G from above is
37. 37. Taking the total differential, we have Replacing dU with the result from the first law gives
38. 38. Applications of Gibbs Free Energy Colligative properties of solutions Boiling point elevation and freezing point depression The pressure on a liquid affects its volatility Electron-free energy levels
39. 39. Effect of pressure on a liquid Applying hydrostatic pressure to a liquid increases the spacing of its microstates, so that the number of energetically accessible states in the gas, al though unchanged, is relatively greater— thus increasing the tendency of molecules to escape into the vapor phase. In terms of free energy, the higher pressure raises the free energy of the liquid, but does not affect that of the gas phase.
40. 40. Thermodynamics of rubber bands Rubber is composed of random-length chains of polymerized isoprene molecules. The poly(isoprene) chains are held together partly by weak intermolecular forces, but are joined at irregular intervals by covalent disulfide bonds so as to form a network..
41. 41. Conti’ The intermolecular forces between the chain fragments tend to curl them up, but application of a tensile force can cause them to elongate The disulfide cross-links prevent the chains from slipping apart from one another, thus maintaining the physical integrity of the material. Without this cross-linking, the polymer chains would behave more like a pile of spaghetti.
42. 42. Example Hold a rubber band (the thicker the better) against your upper lip, and notice how the temperature changes when the band is stretched, and then again when it is allowed to contract. a) Use the results of this observation to determine the signs of ΔH, ΔG and ΔS for the process rubberstretched → rubberunstretched b) How will the tendency of the stretched rubber to contract be changed if the temperature is raised?
43. 43. Solution  a) Contraction is obviously a spontaneous process, so ΔG is negative. You will have observed that heat is given off when the band is stretched, meaning that contraction is endothermic, so ΔH > 0. Thus according to ΔG = ΔH – TΔS, ΔS for the contraction process must be positive. b) Because ΔS > 0, contraction of the rubber becomes more spontaneous as the temperature is raised.