By : Ms. Nor Helya Iman Bt Kamaludin CHAPTER 8 BALANCES ON NONREACTIVE PROCESSES 1 PTT 108: Mass and Energy Balances

Introduction Non-reactive processes  Processes that undergo without chemical reaction.  Depends on the physical/environmental factors like temperature, volume, pressure, boiling and melting, as well as vaporization. Normally in chemical process unit, W s =0; Δ E p =0; Δ E k =0; Then energy balance equation become: Close System Open System 2 PTT 108: Mass and Energy Balances

Different symbols between close and open system PTT 108: Mass and Energy Balances 3 CLOSE SYSTEMOPEN SYSTEM n (amount) (molar flow rate) U (internal energy) (rate of enthalpy) Û (specific internal energy) (specific enthalpy)

Introduction (cont’d) PTT 108: Mass and Energy Balances 4 For this chapter, we will learn the procedure for evaluating Δ U and Δ H when table Ĥ and Û are not available for all process species. Example enthalpy change ( Δ Ĥ ) for solid phenol at 25 ˚C and 1 atm converted to phenol vapor at 300 ˚C and 3 atm.

Introduction (cont’d) PTT 108: Mass and Energy Balances 5 To evaluate changes in enthalpy or internal energy, we can make up any process path we want to simplify the calculations. They can often be evaluated for: 1. changes in P at constant T 2. changes in T at constant P 3. changes in T at constant V 4. changes in phase at constant T and P (e.g., heats of vaporization) 5. mixing at constant T and P (heats of mixing) 6. chemical reactions at constant T and P (heats of reaction)- Chapter 9

Hypothetical Process Path PTT 108: Mass and Energy Balances 6 State properties  Properties that depend on the state of the species (primarily on its temperature and state of aggregation, and also pressure).  Specific enthalpy ( Ĥ ) and specific internal energy (Û) are state properties species  When a species passes from one state to another state, both Δ Ĥ and Δ Û for the process are independent of the path taken from the first state to the second state. We can construct a hypothetical process path which can consist of several step based on our convenience, as long as we reach to the final state, starting from their initial state.

Hypothetical Process Path (Examples) PTT 108: Mass and Energy Balances 7 Δ Ĥ = (vapor, 300˚C, 3 atm) – (solid, 25˚C, 1 atm) Cannot determine directly form enthalpy table – must use hypothetical process path consist of several step. Check Table B.1 for Phenol : P= 1 atm; T m = 42.5˚C and T b = 181.4˚C

Procedure Energy Balance Calculations PTT 108: Mass and Energy Balances 8 1. Perform all required material balance calculations. 2. Write the appropriate form of the energy balance (closed or open system) and delete any of the terms that are either zero or negligible for the given process system. 3. Choose a reference state – phase, temperature, and pressure – for each species involved in the process. 4. Construct inlet-outlet table for specific internal energy (close system) or specific enthalpy (open system)  For closed system, construct a table with columns for initial and final amounts of each species (m i or n i ) and specific internal energies relative to the chosen reference states (Û i ).  For an open system, construct a table with columns for inlet and outlet stream component flow rates ( ) and specific enthalpies relative to the chosen references states ( Ĥ i ).

Procedure Energy Balance Calculations (cont’d) PTT 108: Mass and Energy Balances 9 5. Calculate all required values of Ĥ i or Û i and insert the values in the appropriate places in the table. 6. Then calculate Δ Ĥ or Δ Û for the system. Closed System: Open System: 7. Calculate any work, kinetic energy, or potential energy terms that you have not dropped from the energy balance. 8. Solve the energy balance for whichever variable is unknown (often Q or ).

Class Discussion PTT 108: Mass and Energy Balances 10 EXAMPLE 8.1-1: Energy Balance on a Condenser The flowchart

Solution PTT 108: Mass and Energy Balances 11 STEP 1: Perform required material balance calculations. -None are required in this example because there are no material balance involved in this process. STEP 2: Write and simplify the energy balance. For open steady-state system:

PTT 108: Mass and Energy Balances 12  Delete any of the terms that are either zero or negligible in process system. -No moving parts and no energy is transferred in the system: -No significant vertical distance separates the inlet and outlet ports: -Phase changes and nonnegligible temperature changes occur: So, the energy balance become:

PTT 108: Mass and Energy Balances 13 STEP 3: Choose reference states for acetone and nitrogen. N 2 (g, 25˚C, 1 atm) : convenient (Table B.8) Ac (l, 20˚C, 5 atm) : choose from one of the process stream. STEP 4: Construct an inlet-outlet enthalpy table. References: Ac (l, 20˚C, 5atm); N2 (g, 25˚C, 1atm)

PTT 108: Mass and Energy Balances 14 STEP 5: Calculate all unknown specific enthalpies In this step we need to find i. For changes in pressure (∆P) at constant T ii. For changes in temperature (∆T) at constant P iii. For changes in phases at constant P and T Use heat of vaporization or heat of melting at normal boiling point and normal melting point, respectively. (can be obtained from Table B.1)

PTT 108: Mass and Energy Balances 15 The process path involved for determination of = ( ) kJ/mol = 35.7 kJ/mol *Use the same manner to obtain the values for

PTT 108: Mass and Energy Balances 16 -insert all specific enthalpies into inlet-outlet enthalpy table STEP 6: Calculate

PTT 108: Mass and Energy Balances 17 STEP 7: Calculate nonzero work, kinetic energy and potential energy terms -no need to be calculated since there are no shaft work and we are neglecting kinetic and potential energy. STEP 8: Solve the energy balance for = kJ/s = kW Heat must be transferred from the condenser at a rate of kW to achieve the required cooling and condensation.

Changes in P at Constant T (no phase change or reactions) PTT 108: Mass and Energy Balances 18 Ideal gases: Independent of pressure ( unless undergo very large pressure changes) Real gases: must evaluate from: 1. enthalpy departure charts 2. an equation of state 3. tabulated data Liquids and solids: Nearly independent of pressure

Changes in T and Constant P (no phase change or reactions) PTT 108: Mass and Energy Balances 19 Called sensible heat, heat that must be transferred to RAISE or LOWER the temperature of substance or mixture of substance and we usually find: Heat capacities help us calculate this change in enthalpy. The “heat capacity at constant pressure” is defined by: Thus, enthalpy changes at constant P are given by integration of this equation:

Changes in T and Constant P (no phase change or reactions) PTT 108: Mass and Energy Balances 20

Changes in T at Constant V (no phase change or reactions) PTT 108: Mass and Energy Balances 21 Here, we use the heat capacity at constant volume, defined by: Ideal gases: Liquids and solids:

Heat Capacity Formulas PTT 108: Mass and Energy Balances 22 Definition: Heat capacities, C p and C v are physical properties of materials and are tabulated in standard references. Units: J/(mol.K) and Btu/(lbm.˚F) Relationships exist between C p and C v : where R = gas constant

Heat capacity, C p PTT 108: Mass and Energy Balances 23 Estimation of heat capacities, C p  Kopp’s rule- simple empirical method for estimating C p of solid or liquid at or near 20˚C based on the summation of atomic heat capacities (Table B.10) of the molecular compound. (C p ) Ca(OH)2 = (C pa ) Ca + 2(C pa ) O + 2(C pa ) H = 26 + (2x17) + (2x9.6) = 79 J/mol.˚C  Polynomial expressions for C p in Table B.2 based on the experimental data for the listed compound.

Heat capacity, C p (cont’d) PTT 108: Mass and Energy Balances 24 Table B.2 demonstrated the heat capacities as a function of temperature (at low pressures) in the equation form for a number of solid, liquid, and gaseous substances. This is your source of ideal-gas heat capacities. Tables of specific enthalpies eliminate the need for use of heat capacities, i.e., someone has already done the integrations for you. For "combustion gases" you should use the tables of molar enthalpies given in Table B.8 and Table B.9.

Heat capacity, C p (cont’d) PTT 108: Mass and Energy Balances 25 Mixtures: Where = heat capacity of the mixture = mass or mole fraction of the ith component = heat capacity of the ith component

Class Discussion PTT 108: Mass and Energy Balances 26 EXAMPLE EXAMPLE EXAMPLE EXAMPLE EXAMPLE 8.3-5

Phase Change Operations PTT 108: Mass and Energy Balances 27 Phase change such as melting and evaporation are usually accompanied by large changes in internal energy and enthalpy Latent heat  Specific enthalpy change associated with the transition of a substance from one phase to another at constant T & P. Heat of fusion or heat of melting, Δ Ĥ m (T,P)  Specific enthalpy different between solid and liquid forms of species at T & P  Heat of solidification (liquid to solid) is –ve value of heat of fusion. Heat of vaporization, Δ Ĥ v (T,P)  Specific enthalpy different between liquid and vapor forms of species at T & P  Heat of condensation (vapor to liquid) is –ve value of heat of vaporization. The latent heat of phase change may vary considerably with the temperature at which the changes occurs but hardly varies with the pressure at the transition point.

Estimation of Heat of Vaporization PTT 108: Mass and Energy Balances Trouton’s rule – accuracy between 30% 2. Chen’s equation – accuracy between 2% 3. Clausius-Clapeyron equation - plot In p* versus 1/T

Estimation of Heat of Vaporization (cont’d) PTT 108: Mass and Energy Balances Chaperon equation 5. Watson correlation – estimate Δ Ĥ v at T 2 from known Δ Ĥ v at T 1 Estimation of Heat of Fusion Δ Ĥ m (kJ/mol) = T m (K) metallic elements = T m (K) inorganic compound = T m (K) organic compound

Class Discussion PTT 108: Mass and Energy Balances 30 EXAMPLE EXAMPLE EXAMPLE EXAMPLE 8.4-4

Psychrometric Charts PTT 108: Mass and Energy Balances 31 PSYCHROMETRIC chart (or HUMIDITY Chart) is a compilation of a large quantity of physical property data in a single chart. The properties are: (a) Wet Bulb Temperature (b) Saturation Enthalpy (c) Moisture Content (d) Dry Bulb Temperature (e) Humid Volume The Psychrometric Chart is particularly important for Air- Water system and normally is at Pressure of 1 atm. Psychrometric Chart is very useful in the analysis of humidification, drying, and air-conditioning process.

PTT 108: Mass and Energy Balances 32

Psychrometric Charts (cont’d) PTT 108: Mass and Energy Balances 33 To use Psychrometric Chart, you need to know TWO values to determine the values of the others on the chart. IMPORTANT TERM: Dry-bulb temperature, T – This is the air temperature as measured by thermometer, thermocouple, or other conventional temperature measuring device. Absolute humidity, h a [kg H 2 O(v)/kg DA] – Called moisture content placed on the ordinate of the chart.

Psychrometric Charts (cont’d) PTT 108: Mass and Energy Balances 34 Relative humidity, h r Curves on the psychrometric chart correspond to specified values of h r (100%, 90%, 80%, etc.). The curve that form the left boundary of the chart is 100% relative humidity (saturation curve). Dew point, T dp The temperature at which humid air becomes saturated if it is cooled at constant pressure. Humid volume, (m 3 /kg dry air) The humid air is the volume occupied by 1 kg of dry air plus the water vapor that accompanies it.

Class Discussion PTT 108: Mass and Energy Balances 35 EXAMPLE 8.4-5

THANK YOU…. PTT 108: Mass and Energy Balances 36