Thermodynamics Notes PDF

# Thermodynamics ## Chapter (1): Introduction ### Part (1) 2024-2025 M.F ## Chapter (I): Basic Defination ### Thermodynamics Thermo Heat (Energy)= Dynamic transfer= Branch of Science which studies the transfer of Energy (Heat) from one place to another. ### Chemical Thermodynamics: Study the hea...

# Thermodynamics ## Chapter (1): Introduction ### Part (1) 2024-2025 M.F ## Chapter (I): Basic Defination ### Thermodynamics Thermo Heat (Energy)= Dynamic transfer= Branch of Science which studies the transfer of Energy (Heat) from one place to another. ### Chemical Thermodynamics: Study the heat transfer accompined the Chemical Reaction. ### NB: Thermodynamics Can be determined the position of Chemical equilibrium M.F ## Chapter (I): Basic Defination ### Application of Thermodynamics 1. Design of Engines 2. Metabolism of Food 3. Study heat absorbed or evolved From reaction 4. Decide the reaction: Spontaneous, Non-Spontaneous ### Laws of thermodynamics: 1. Zero Law: Define temperature 2. 1st Law: State of Energy Conservation 3. 2nd Law: Define Entropy 4. 3rd Law: Entropy of pure solid standard condition ### Thermodynamics Terms: A. System B. Surrounding C. Boundary (wall) C. Work (W) D. Heat (q) ### System: The macroscopic part of universe under study in thermodynamics. ### Surrounding: The rest of universe which in direct contact with System. ### Boundary: Surface dividing System and Surrounding. ### Work (W): Product of Force (F) and distance (d) W= F.dr ### Heat (q): Form of Energy transfer From high Temp object to low Temp object. ### Internal Energy (E) Internal energy of System is Changed by: 1. Heat absorbed or evolved by System. 2. Work done on or by System. 3. Mass enters or leaves the system. ### Types of Walls: 1. Permeable wall: Transfer both Energy and matter dw≠0 .dq≠0 .dm≠0 2. Impermeable wall: Transfer Energy only not matter. dw≠0.dq=0.dm=0 3. Adiabatic wall: Not transfer heat and matter dw≠0.dq=0.dm=0 4. Rigid wall: Has Fixed Shape and position. ### Types of System: | System | Wall | Properties | |:--------|:------------|:--------------------------------------------| | Open | Permeable | • Transfer Heat, Work and mass. | | | | • dm≠0 .dq≠0 .dw≠0 | | | | • Internal energy Changed | | Closed | Impermeable | • Transfer heat and work not mass. | | | | • dm=0 .dq≠0 .dw≠0 | | | | • Internal energy Changed.(due to q and W) | | Adiabatic | Adiabatic | • No transfer heat or matter. | | | | • Transfer work only. | | | | • dm= 0 .dq=0 .dw≠0 | | | | • Internal energy Changed due to work only. | | Isolated | Adiabatic | • No transfer Energy or matter | | | | • No interaction between System and Surrounding | | | | • dm=0.dq=0.dw=0 | | | | • Internal energy not Change | ### Types of thermodynamics Process Change of System state from initial to Final 1. **Isothermal Process:** • Temperature is Constant⇒dT=0 2. **Isobaric Process:** • Pressure is Constant:dP=0 3. **Isochoric Process:** • Volume is Constant: dV=0 4. **Adiabatic Process:** • No heat or mass Transfer dq=0 5. **Cyclic Process:** (initial and Final Same) • T= Const (Tf=Ti) • P= Const (Pf=Pi) • V= Const (Vf=Vi) ### 6. Reversible • Slow process • Very Small Changes • Large no of steps • Equilibrated steps • Can be reversed ### 7. Irrevesible • Fast process • Sudden Change • One Step (spontaneous) • No chance to attain the equilibrium. • Natural Process == ### Thermodynamics Equilibrium: When Properties of System like T, P and V are Constant with time. ### A. Thermal Equilibrium: No Change in properties of System and Surrounding When Seperated by thermal Conducting wall. • T is Constant == ### B. Chemical Equilibrium: Composition (Concn)= Constant ### C. Mechanical Equilibrium: No acceleration and no turbulence. P is Constant == ### Physical Properties of System: | Type | Properties | |:-------|:-----------------------------------------------------------------------------------| | Extensive | • The properties which depend on quantity of matter in system (amount extent size) | | Intensive | • Properties independant on quantity of matter in System. | #### Extensive Examples: • Mass • Volume • Heat • Heat Capacity • Enthalpy • Free Energy • Entropy • No of moles. #### Intensive Examples: • Density • Viscosity • Pressure • F.p • B.p • m.p • Partial molar quantites • Refractive index • Temp • Chemical potential • Surface Tension • Specific heat. ### Types of Functions: | Function | State | Path | |:----------------|:-----------------------------------------------|:-----------------------------------------------| | Depend on | • Initial and Final state | • Path of Process | | Symbol | • Write in Capital letters | • Write in Small letters | | Differentiate | • dx is total differential | • dx is Partial differential | | Integration | • Integration with limits | • Integration without limits | | | X2 | X2 | | | • ∫f(x)dx = X2-X1 = AX | •∫ f(x)dx = X one value | | | X1 | | | Cyclic Process | • ∫f(x)dx = X1-X1=0 | • ∫f(x)dx = X | | Examples | A, T, E, H, P, S, G, q and W | | **Note:** (important) All thermodynamics Functions are state except Heat (q) and work (W)⇒ Path Functions. ### Revision #### 1. Differentiation: (3 Rules) • d/dx Xn = nX^(n-1) • EX: d/dx X^4 = 4X^3 • d/dx 2X^3 = 6X^2 • d/dx y^2 = zero (due to y is Constant) • d/dx (Xn) = d/dx X^n = -nX^(n-1) • EX: d/dx X^-2 = d/dx X^-2 = -2X^-2-1 = -2X^-3 **Quiz:** • d/dx (X^2+3X+Y^2 ) = ?? • d/dx (1/X)= ?? #### 2. Integration | Type | Without limits | With limits | |:---------------------|:------------------------------------------------|:------------------------------------------------| | 1. | ∫fdx= X + Const | ∫fdx=X2-X1 = ΔX | | 2. | ∫X^n dx =(X^(n+1))/(n+1) + Const | ∫X^n dx = (X2^(n+1)/(n+1)-(X1^(n+1)/(n+1)) | | 3. | ∫(1/x)dx= lnX+C | ∫(1/x)dx = lnX2-lnX1= ln(X2/X1) | | log and ln (same for log) | • lnA+lnB = ln AB | | | | • lnA-lnB= ln (A/B) | | | | • ln AB = B*lnA | | ### Euler Theorem (reciprocity relation) • To determine Type of Function (state of Path): • IF Z=f(x,y) • ∴dz = (∂Z/∂y)ydx + (∂Z/∂x)xdy • (∂Z/∂y)y=M • (∂Z/∂x)x=N Then • (∂M/∂y)x = 1 and (∂N/∂x)y =2 | Cases | Z is a state Function (Exact differential) | Z is a path Function (not exact differential) | |:--------|:-------------------------------------------|:------------------------------------------------| | 1=2 | ☑ | | | 1≠2 | | ☑ | • ∂^2Z / ∂x∂y = ∂^2Z / ∂y∂x ### Fouad Method To solve Euler problems to know the function type (state or path), we follow these steps: 1. Write the given equation, making sure that the function is on one side and the variables on the other side. For example: Z=XY. 2. Write the variables that the function depends on. (Z = f(X,Y) known from the given equation). 3. Write the change equation: dZ= (∂Z/∂Y)ydX + (∂Z/∂X)xdy I. Differentiate Z with respect to X. II. Differentiate Z with respect to Y. • Determine the value of the first parenthesis (∂Z/∂Y) by removing Z and substituting its value from the equation (1), then differentiate the equation with respect to Y, considering X as a constant. • The outcome of the differentiation will give you a new equation, and we will call it N. • Differentiate the new equation N with respect to the other variable, X, and keep the first variable Y constant (we are reversing the variables). Doing so, we will get the value of (∂N/∂Y)x. • Determine the value of the second parenthesis (∂Z/∂X) by removing Z and substituting its value from the equation (1), then differentiate the equation with respect to X, considering Y as a constant. • The outcome of the differentiation will give you a new equation, and we will call it M. • Differentiate the new equation M with respect to the other variable, Y, and keep the first variable X constant (we are reversing the variables). Doing so, we will get the value of (∂M/∂X)y. • If (∂M/∂X)y = (∂N/∂Y)x: then it’s State. If (∂M/∂X)y ≠ (∂N/∂Y)x: then it’s not a state. ### Ex (1): If Z=17X^4Y + 22X^2Y^5, show if Z is a State Function or not. **Answer** 1. Z=17X^4Y+22X^2Y^5 2. Z= f(X,Y) 3. ∴ dz= (∂Z/∂Y)ydX + (∂Z/∂X)xdy • (∂Z/∂Y)y=M=?? • (∂Z/∂X)x=N=?? • M=(∂(17X^4Y + 22X^2Y^5)/∂Y) • M= 68X^3Y^4 + 22Y^5 • (∂M/∂Y)x = (∂( 68X^3Y^4 + 22Y^5)/∂Y)x • (∂M/∂Y)x = 68X^3 + 110Y^4 (1) • N=(∂(17X^4Y + 22X^2Y^5)/∂X) • N=17X^4 + 44Y^4X • (∂N/∂X)y = (∂(17X^4 + 44Y^4X)/∂X) • (∂N/∂X)y = 68X^3 + 44Y^4 (2) • (1) = (2) • Z is a State Function • dz is exact differential ### Ex (2): If Z= 4X^2Y^2 + X^3, show if Function Z is state or not. **Answer:** • Z= 4X^2Y^2 + X^3 • Z= f(X,Y) • ∴ dz= (∂Z/∂Y)ydX + (∂Z/∂X)xdy • (∂Z/∂Y)y= M=?? • (∂Z/∂X)x=N=?? • M=( ∂(4X^2Y^2 + X^3)/∂Y)y • M= 8XY^2 + 3X^2 • (∂M/∂Y)x = (∂(8XY^2 + 3X^2)/∂Y)x • (∂M/∂Y)x= 16XY (I) • (∂Z/∂X)x=(∂(4X^2Y^2 + X^3)/∂X)x • N= 8XY^2 • (∂N/∂X)y = (∂(8XY^2)/∂X)y • (∂N/∂X)y = 16XY (II) • I=II • Z is a State Function • dz is exact differential ### Ex (3): If dZ= 4X^2Y^2dX+3X^2Ydy, show if dz is exact differential or not: **Answer:** • Z= f(X,Y) (1) • ∴ dZ= (∂Z/∂Y)ydX + (∂Z/∂X)xdy (2) • ∴ dZ= 4X^2Y^2dX+3X^2Ydy (given) (3) • Compare equation (2) and (3): • (∂Z/∂Y)y= 4X^2Y^2 = M • (∂Z/∂X)x= 3X^2Y= N • (∂M/∂Y)x = (∂(4X^2Y^2)/∂Y)x • (∂M/∂Y)x = 8XY^2 (I) • (∂N/∂X)y = (∂(3X^2Y)/∂X)y • (∂N/∂X)y = 6XY (II) • I≠II • ∴ dz is not exact differential ### Quiz: **Choose the correct answer:** 1. The system at which no change in internal energy: a. Adiabatic b. Isolated c. Closed d. Open 2. Which of the following state function: a. q b. w c. T 3. Which is correct for cyclic process : a. dw=0 b. ΔE=0 c. dW≠0 4. Which of the following is an intensive property: a. Volume b. Mass c. B.P d. Concentration 5. Work can be done in ................system a. Open b. closed c. Adiabatic d. all of them 6. A system that transfer matter and energy to its surrounding a. Reversible b. Isolated c. Closed d. Open 7. If x is a path function, then: a. ∫dx= 0 b. ∫x dx = ΔX c. ∫x dx = X2-X1 8. The Reversible process is.... a. Stepwise b. equilibrated steps c. slow 9. For adiabatic system......... a. dw ≠ 0 b. dq ≠ 0 c. dE ≠ 0 10. For Isolated system.......... a. dw=0 b. dm=0 c. dE = 0 11. For function Z= 4X^3Y^3+2X^2Y^4 : a. Z is state function b. Z is path function 12. The sum of system and surrounding is... a. Wall b. boundary c. universe 13. The wall has fixed dimension is .... a. Permeable b. Impermeable c. Adiabatic 14. The system at which only work done (dw≠ 0) is : a. Open b. close c. adiabatic 15. The system that transfers energy not mass is : a. Open b. close c. adiabatic 16. The wall of open system is : a. Impermeable b. permeable c. rigid wall 17. The process at which final state and initial state are the same is : a. Isothermal b. adiabatic c. reversible 18. The process at which pressure is constant (dP=0 ) : a. Isochoric b. isobaric c. isothermal 19. The process which contain equilibrium between each step and the following step : a. Isothermal b. adiabatic c. reversible 20. The process at which occur at sudden change is : a. Isochoric 21. The process at which occur at slow changes is : a. Isochoric b. reversible c. isothermal 22. For first differential function dZ=12X^2Y^3 dX + 12X^3Y^2 dY a. Z is state function b. Z is path function 23. Which of the following is a not a state function : a. Z=2XY+4X^2Y^2 b. Z= X^3Y^4 24. Which of the following is extensive physical property: a. Temperature b. specific heat 25. Which of the following is intensive physical property: a. Volume b. specific heat c. Heat capacity 26. Which of the following is extensive physical property: a. Internal energy b. specific heat 27. For adiabatic system : a. dw=0,dq=0, dm=0 b. dw≠0,dq≠0, dm=0 28. For open system : a. dw=0,dq=0, dm=0 b. dw≠0,dq≠0, dm=0 29. For closed system : a. dw=0,dq=0, dm=0 b. dw≠0,dq≠0, dm=0