Reflection. Review of Energy Balances. Class 28. Concepts. Professional Program Application. After Action Report
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1 Reflection After Action Report What did I learn from this W assignment? Professional Program Application Meet with you advisor an form Pink Form Excel course planning worksheet Due November 7! Note: Any Bio class that satisfies GE can be used, not just Bio 00 Professors cannot do this all on the last day, so start early!! Application required before you can get an add code for ChEn 374 (Fluids) Review of Energy Balances Class 8 Enthalpies, eat Capacities eats of Formation, Oh My! Enthalpies needed to calculate heat or work terms Methods to calculate enthalpy (so far): Steam tables Graph (P- diagram) Interpolation from given values Needed: Method to get enthalpies for any species as a function of & P Concepts Concept. Enthalpy Is A State Function. Enthalpy is a state function. eat Capacities 3. Latent eats (phase change) 4. eat of Formation 5. Calculating as f(,p) P Rankine cycle (most common method to generate electricity!) is the same here regardless of path Enthalpy is independent of path Always talk about from some reference condition Steam tables: 0at triple point Other tables are different (e.g., in able B., for = 0 at 5C) Don t mix and match tables!!!
2 Concept. eat Capacities Concept. eat Capacities (cont.), d, d Now define heat capacities:, For ideal gases:, For solids and liquids: d Generally small C p not linear area = like slope of vs curve, prob 7.5 so 3 4 For ideal gases: C p = C v + R For solids and liquids, A Practical View Wouldn t it be nice to have a polynomial equation for! = a + b + c his would not work for different reference enthalpies! Solution: Polynomial for C p C P = a + b + c + d (= d/d) Fit to thermodynamic data 0.08 (kj/mol) vs. for Benzene gas Cp (kj/(mol*deg C) (deg C) Cp vs for Benzene gas (deg C) Caution! When getting a heat capacity coefficient from able B., use the multiplier at the top of the column Example: Acetone a = 3 multiplier = 0 3 (i.e., the actual number was multiplied by 0 3 to make it look nicer in the table) herefore, a = kj/(gmolk) C p Integrated form: DIPPR Format C A B sinh D C coshe E C C E E BC coth coth DE tanh C pd A tanh
3 Concepts. Enthalpy is a state function. eat Capacities 3. Latent eats (phase change) 4. eat of Formation 5. Calculating as f(,p) Concept 3. Phase Changes (pure substances) melt ice liquid vap gas Slope = (tabulated) (tabulated) Also we could find Remember that for a pure substance, is constant during a phase change Kopp s Rule: C p kc p, k kelement where k = moles of element k in molecule So for solid phenol, C 6 5 O, C = 6 = 6 O = C p = 6* * = 9.6 J/(mol C) (Dippr = 9 J/(mol C) at 5C) Only use this out of desperation! Other Estimation Formulas routon s rule (8.4-3) v = f( b ) Chen s equation (8.4-4) v = f( b, c, P c ) Clapeyron equation (8.4-7) v = f(p*) Watson s correlation (8.4-8) v vs. using c Only use these equations out of desperation! 3
4 Simplifications Concepts Sometimes we get lazy and assume an average heat capacity for some temperature range = We will use this on exams! I am not testing you on integration skills. Enthalpy is a state function. eat Capacities 3. Latent eats (phase change) 4. eat of Formation 5. Calculating as f(,p) Concept 4. eat of Formation Wanted: Common reference state for all species! Can use as a reference at 5C, atm Good for reaction chemistry = 0 for species whose natural state is 5C, atm N, O,, C(graphite),, abulated in able B. Balances wo Methods to Get. Path Method 4,, 3 98, 98 where a i, b i, and c i are the heat capacity coefficients for species i 98 3 Note that for a chemical reaction, the number of moles of each species (n i ) changes. f0 method,, So compute 4 and and subtract 4
5 Example Example: Find for acetone vapor at 65C forming a liquid at 0 C and 5 atm (Path method) Calculate the enthalpy change for acetone going from a vapor at 65C and atm to a liquid at 0 C and 5 atm A. Path method using vap at atm and boiling B. eat of formation method a Acetone (vapor) 65C, atm, Acetone (vapor) 56C, atm = =? c b 0C, 5 atm 0C, atm, 56C, atm,,, Example: Find for acetone vapor at 65C forming a liquid at 0 C and 5 atm ( fo method) Bottom Line Acetone (vapor) 65C, atm,, = =?,, 0C, 5 atm You Should Know Both Methods to Get. Path Method. fo method,,,, 5,,,, Remember that is just part of energy balance 5
6 aboo Equations 3 rd Edition Page 45: 9.5-a and 9.5-b st Eqn. on page 457 Page 463: last equation (under section 5) 4 th Edition Page 506: 9.5-a and 9.5-b st Eqn. on page 5 Page 59: last equation (under section 5) Problem Solving (pp ). Solve material balances (mass or moles). Write energy balance (drop appropriate terms) 3. Choose reference state(s) 4. able of n i & i in and out (or m i, U i, etc.) 5. Find sys or U sys 6. Find W, W s, E k, E p as needed 7. Solve energy balance omework Problems int on Prob 8. PV = nr QUIZ. What is meant by the statement that enthalpy is a state function?. What is a heat capacity? 3. For water, draw a graph with temperature on the y axis and enthalpy on the x axis, starting from ice and proceeding to steam, labeling the different portions of the line. 4. ow do you use the heat of formation to calculate enthalpy? (eqn. needed). What is meant by the statement that enthalpy is a state function? is not dependent on & P path. What is a heat capacity? Change in enthalpy with temperature 3. For water, draw a graph with temperature on the y axis and enthalpy on the x axis, starting from ice and proceeding to steam, labeling the different portions of the line. ice melting boiling water steam. ow do you use the heat of formation to calculate enthalpy? melt ice liquid vap gas Slope = 6
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