Practice Midterm Exam 1 March, 2011

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1 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 Grand Total: - next page 1

2 - next page 2 NAME:

3 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 3

4 4. Derive a relationship that describes the dependence of Gibb's Free Energy upon temperature and volume. 5. 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 6. 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 5 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 7. 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 8. The relationship between C v and C p given is by: 2 TV CV CP Using this relationship, derive the relationship between C v and C p for an ideal gas for which n is not equal to one. 7

8 9. Given the following coefficient, fully derive the related state function. F S. T The state function should be simplified as much as possible and include as many materials parameters as possible (i.e., toolbox 2). Show all steps to receive full credit. Hint: your answer should have a C v term in it. 8

9 10. Without using toolbox 3, derive the following state variables as a function of T & P: a. volume b. entropy 9

10 11. For the following reaction, answer the following questions using the information provided to assist you: Al + O 2 Al 2 O 3 298K 298K 1 2 C p a b x 10 3 c x 10-5 Temp. Range H k S k H Xform [J/(mol K)] [K] [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. Sketch the rxn S diagram assuming the reaction will occur as shown. Label all important aspects of the diagram. (5 pts) 10

11 c. Write the symbolic equation (no numbers) down for S products have temperature intervals. (6 pts). Integrals should d. Write the symbolic equation (no numbers) down for Sreactants have temperature intervals. (6 pts). Integrals should 11

12 12. Write down the general expression for Srxn 13. Describe how you would determine Grxn and write down the general equation for Grxn. 12

13 14. For the system, L, the following are the vapor pressures for the condensed-vapor phase equilibria: A D ln p B lnt C 2 T T A D ln p B lnt C 2 T T AL DL ln pl BLlnT CL 2 T T Using these equations and the Clapeyron and Clausius-Clapeyron equations, do the following: a. Draw a T versus P diagram. b. Derive an equation to solve for the normal boiling point temperature. c. Derive equations for both the triple point temperature and pressure. 13

14 d. Derive equations for H V, H V and L V H. 14

15 e. Derive equations for C V, C V and L V C. 15

16 f. Derive equations for H, H L and H L. 16

17 g. Derive an equation for C, C L and C L 17

18 15. Starting with the Clapeyron equation, derive a general equation for the normal melting point for a particular material for two conditions: S L a. Assume both V S L and H are not a function of temperature. Also S L assume that V can be found in the literature (i.e., just leave as S L V in the formula you obtain). 18

19 S L b. Assume V S L is not a function of temperature and that H is a S L function of temperature. Also assume that V can be found in the S L literature (i.e., just leave as V in the formula you obtain). 19

20 16. 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

Practice Midterm Exam 1 March, 2005

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 1. 2.