Practice Midterm Exam 1 March, 2005

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1 NAME: MSE 308: Thermodynamics of Materials Department of Materials Science & Engineering Boise State University Spring 2005 Practice Midterm Exam 1 March, 2005 Problem Total Points Points Obtained Grand Total: - next page 1

2 NAME: 1. Write down the mathematical equations for the 1 st and 2 nd laws of thermodynamics. Describe each law with one sentence each. (5 points) 2. Write down the equation describing the combination of the 1 st and 2 nd laws of thermodynamics (otherwise known as the Fundamental Equation of Thermodynamics - FEOT). Is this equation an exact or inexact differential? (4 points) 3. Write down the functionality, i.e., Z = Z(x,y), of the FEOT. (2 points) - next page 2

3 4. The notion of a "reversible" process is a fiction in the real world. What makes this concept, which at first glance would appear to be only of academic interest, so useful in applying thermodynamics to real-world "reversible" processes? Limit your answer to no more than 3 succinct sentences. (3 points) 3

4 5. Derive a relationship that describes the dependence of Gibb's Free Energy upon temperature and volume. 6. Using your answer from developing a relationship that describes the dependence of Gibb's Free Energy upon temperature and volume, derive an expression if you consider the system you are dealing with is an ideal gas with n not equal to one. 4

5 7. Using a graph of volume and temperature to assist you, explain with words and equations (do not solve them) how you would use your answer in problem 6 to find the Gibb's Free Energy change from some initial state to some final state. Be succinct in your explanation. (7 points) 5

6 8. Derive the differential equation for the change in volume when the entropy of n moles of an unknown gas increases to twice its original value and the Gibb's free energy decrease by half of its initial value. Circle all answers including the coefficients you have derived and your derived general equation. (13 points) 6

7 9. Use the differential you obtained in the previous problem to derive the differential assuming the gas is an ideal gas. Remember that C v for an ideal gas is 3 2 nr. Simplify your answer as much as possible. Circle your answer. (7 points). (20 points) 7

8 10. Draw a plot showing the process path you would take to find V. Label each process path. (? points) 8

9 11. Using your plot and process paths, derive V (i.e., perform the integrations). State each process path for each integration. (? points) 9

10 12. The relationship between C v and C p given is by: 2 TVα CV = CP β Using this relationship, derive the relationship between C v and C p for an ideal gas for which n is not equal to one. 10

11 13. The rather mundane material Borium (Bo) has the following properties: a. C p = a + b T b. α = thermal expansion coefficient c. β = compressibility d. V = molar volume e. Bo is solid over all temperatures of interest to us here. Express the pressure required to keep the volume of one mole of Bo constant when the temperature in increased from 298K to T, in terms of T and the materials properties. Assumptions: α and β are very small numbers. 11

12 14. Without using toolbox 3, derive the following state variables as a function of T & P: a. volume b. entropy 15. For the following reaction, answer the following questions using the information provided to assist you: C p [J/(mol K)] Al + O 2 = Al 2 O 3 a b x 10 3 c x 10-5 Temp. Range [K] 298K H k 298K S k 1 2 H Xform [kj/mol] [J/(mol K)] [kj/mol] Al (s) (T m ) Al (l) (T b ) Al (g) O 2(g) Al 2 O 3(s) (T m ) Al 2 O 3(l) unknown a. Balance the reaction equation. (3 points) b. Draw the S rxn diagram. Label all important aspects of the diagram. (5 pts) 12

13 c. Write the symbolic equation (no numbers) down for S products. Integrals should have temperature intervals. (6 pts) d. Write the symbolic equation (no numbers) down for Sreactants have temperature intervals. (6 pts). Integrals should 13

14 16. Write down the general expression for Srxn 17. Describe how you would determine Grxn and write down the general equation for G rxn. 14

15 18. Using the Clapeyron equation, derive the Clausius-Clapeyron equation. State all assumptions that you are making. 19. Draw a P vs T phase diagram given the following system: α β δ γ L ν with α being the lowest temperature phase. 15

16 20. For the system, α β δ γ L ν, the following are the vapor pressures for the condensed-vapor phase equilibria: Aα ln pα = + Bα lnt + Cα T Aβ ln pβ = + Bβ lnt + Cβ T Aδ ln pδ = + Bδ lnt + Cδ T Aγ ln pγ = + Bγ lnt + Cγ T AL ln pl = + BLlnT + CL T Using these equations, do the following: a. Describe a method and derive equations to find the triple point pressure and temperature for the δ γ ν triple point. b. Describe a method and derive equations to find the boiling point pressure and temperature for the δ γ ν triple point. 16

17 c. Describe a method and derive equations to find the H β δ. d. Describe a method and derive equations to find C β δ p. 17

18 21. On April 15 th of last year, you performed experiments to determine the heat of vaporization of the element Taxinium. From your measurements, you have acquired the data tabulated in table 2. From this data, calculate the heat of vaporization ( H vap ). Assume the H vap is not a function of temperature and thus has Arrhenius behavior. Provide a rough sketch and label all important aspects including the slope. Show all work. (10 points): Table 2: Vaporization data for Taxinium. Temperature (K) Pressure (atm) x x

19 22. Using the definition of S and Ω, where: S = k b ln Ω and n! Ω=, Π r i= 0ni! use Sterling s approximation, given by: ln x! xln x x, to derive: r ni S kb niln. n i= 0 19

Practice Midterm Exam 1 March, 2011

NAME: MSE 508: Solid State Thermodynamics Department of Materials Science & Engineering Boise State University Spring 2011 Practice Midterm Exam 1 March, 2011 Problem Total Points Points Obtained 1. 2.