Project Presentations Groups 1-4 First 40 minutes (10 min/ea) Lecture 6 Goals Ch. 8.1c, 8.3b, 8.3d, 8.4a-b p. 361-365, 369, 373-377 Understand when cp and cv correlations are exact, approximate, and inaccurate. Understand relationship between cp and cv for ideal gases, liquids, and solids. Construct hypothetical process paths for processes with changes in P and T. H, U: State Properties P T 1 2 A B C Does path A = path B + C? Yes. If we calculated DHA would it = DHB+C? Yes. We can calculate DH or DU for any process if we can construct a path using data that can be found in tables or calculated. What kinds of paths can we find in tables or calculate? 1. Change P at Constant T (can be calculated) 2. Change T at Constant P (can be calculated) 3. Phase change at Constant T & P (Tabulated) 4. Mix components at Constant T & P (Tabulated) React components at Constant T & P (Tabulated/Calculated) (1) Changes in P at Constant T ?U ? f(P) for solid or liquid at const T. What is ?U? What is ?H? Most liquids and solids are fairly incompressible: (1) Changes in P at Constant T ?U and ?H ? f(P) for ideal gas. What is ?U? What is ?H? When is this not true? T << 0?C or P >> 1 atm (1) Changes in P at Constant T For non-ideal gas: Calculate z (compressibility, p. 206) or obtain from compressibility charts. If z ? 1, gas is close to ideal, can assume ?U = ?H = 0. If z ? 1 then use tables (Perry?s Handbook) or thermodynamic correlations (more on this in thermo!) (2) Changes in T at Constant P As ?T ? 0, ?U/?T (slope of curve) ? cv cv= heat capacity at constant volume Is cv f(T)? Yes, slope changes with T. (2) Changes in T at constant P What if V ? constant? Is ?U(V1?V2) = 0? Ideal gas? Solid or Liquid? Non-ideal gas? Yes Most of the time No Energy balance on CLOSED systems State 1 U(T, P), Ek, Ep State 2 U(T, P), Ek, Ep Time Q, W Under what circumstances is DU(P,T) = 0? -DT=0, DP=0, and no chemical reaction or phase changes But what if P changes, U(P) sometimes, when is U independent of P? - U ? f(P) if material is ideal gas, and liquids or solids in most situations. (2) Changes in T at constant P What if V ? constant? Is ?U(V1?V2) = 0? Ideal gas? Solid or Liquid? Non-ideal gas? Yes Most of the time No Exact Good Approximation Poor Approx., Good only if V=const. How accurate? (2) Changes in T at constant P What if P ? constant? Is ?H(P1?P2) = 0? Ideal gas? Solid or Liquid? Non-ideal gas? Yes No No Exact Good Approx. Poor Approx., Good only if P = const. Tables or thermo. Slides 5-7 How accurate? Heat Capacities Table B.2 Cp using two forms Pay attention to units d x 1012 = d x 10-12 For ideal gases: For incompressible liquids or solids? How do I get from cp to cv? Worksheet #7A-C Revisited What process path did we construct? Change in P @ Const T (Type 1 Change) Change in T @ Const P (Type 2 Change) What types of changes? Constructing Process Paths What is the process path? Change in P @ Const T (Type 1 Change) Change in T @ Const P (Type 2 Change) is used to make CdTe nanoparticles. What types of changes? Solving Energy Balance Problems Redux Diagram of system labeling all inputs, outputs, knowns, and assumptions. Perform any mass balances. Determine if system is open or closed, select energy balance. Simplify energy balance. Remember Ek of liquid water is << Ek of steam. Look up or calculate thermodynamic data. Solve energy balance (and possibly mass balance). Look up or calculate thermodynamic data. If possible, obtain tabulated data for process changes. If no tables are available, create a process path. Evaluate ?H(specific) or ?U(specific) for each part of the process path. Calculate ?H or ?U using mass or molar flow rates and ?H(specific) or ?U(specific) from part c. Determine ?Htot or ?Utot by adding the contributions from each process path. Worksheet #7 Revisited Tabulated data? Not for exact or close T and P change b) Construct a Path Worksheet #7 Revisited c) Evaluate ?H (specific) for each part of path Worksheet #7 Revisited d) Calculate ?H using mass or molar flow. Worksheet #7 Revisited e) Calculate ?Htot = ??Hpath. Lecture 6 Goals Understand when cp and cv correlations are exact, approximate, and inaccurate. Exact for ideal gas, approximate for liq and sol, inaccurate for non-ideal gas. Understand relationship between cp and cv for ideal gases, liquids, and solids. Ideal gas cp = cv + R, liq, sol cp = cv Construct hypothetical process paths for processes with changes in P and T only. Reviewed Worksheet #7, Te example Ch. 8.1c, 8.3b, 8.3d, 8.4a-b p. 361-365, 369, 373-377 Lecture 6 Goals Perform Energy Balances on Single Phase Systems (Changes in P and T only) Reviewed worksheet #7 Ch. 8.1c, 8.3b, 8.3d, 8.4a-b p. 361-365, 369, 373-377