Chapter 8: Energy Balances on Non-reactive Processes

Lecture 01

ChE 11

Hypothetical Process Path both and are independent of the path

taken from the first state to the second state.

hypothetical process path consists of several step based on our convenience, as long as we reach to the final state starting from their initial/reference state.

Example

4 mol/s H2O

(s, -5C, 1 atm)

4 mol/s H2O

(v, 300C, 1 atm)

Ws (kJ/s)Q (kJ/s)

Method to calculate and associated with certain process

1. Change in P, at constant T & constant phase. (Sec. 8.2 for calculation of H and U)

2. Change in T, at constant P & constant phase. (Sec. 8.3)

3. Phase changes at constant T & constant P

(Sec. 8.4)

4. Mixing at constant T & constant P

(Sec. 8.5 for Hmixture )

5. Chemical reaction at constant T & constant P

(Chapter 9 for Hrxn )

Determine H for each step in the process path

Calculate

Substitute in energy balance to calculate Q - W

steps

toverall HH )(

Hypothetical Process Path from Phenol (s, 25C, 1 atm) to

Phenol (v, 300C, 3 atm) Cannot determine directly form enthalpy table must use hypothetical process

path consist of several step.

Check Table B.1 : P= 1 atm; Tm= 42.5C and Tb= 181.4C

654321 HHHHHHH

True Path

1H

2H

3H

H

4H 5H

6H

Ph (s, 25C, 1 atm)

Ph (s, 42.5C, 1 atm)

Ph (l, 42.5C, 1 atm)

Ph (l, 181.4C, 1 atm) Ph (v, 181.4C, 1 atm)

Ph (v, 300C, 1 atm)

Ph (v, 300C, 3 atm)

Change T, Constant P & Phase

Change Phase, Constant P & T

Change T, Constant P & Phase

Change Phase, Constant P & T

Change T, Constant P & Phase

Change P, Constant T & Phase

Work on this as a group:

Draw a hypothetical path in order to calculate for acetone at (v, 65 C, 1 atm) using a reference state of acetone at (l, 25C, 5 atm).

Determine the specific enthalpy of n-hexane vapor at 200C and 2 atm. (Taking n-hexane liquid at 20C and 1 atm as the reference state).

Work on this as a group:

Calculate the specific enthalpy of carbon monoxide at 450C

Calculate the specific enthalpy of carbon monoxide at 50C

Calculate the rate of cooling, Q required to bring 300 kg/min of carbon monoxide from 450C to 50C using a) Table B.2 b) Table B.8.

Change in P at Constant T & Constant Phase

1.Solid & Liquid

- specific internal energy nearly independent of pressure

2.Ideal Gases

-both specific internal energy and enthalpy independent of pressure (unless undergo very large pressure changes)

PVH

U

0

0

0

H

U

Heat capacity

GasIdealRCC

SolidLiquidCC

vp

vp &

Cp (at constant pressure)/Cv (at constant volume) of a substance are physical properties of material.

Specific Heat. Unit: energy per unit amount per unit temperature. (J/mol.K), (Btu/lbm. F).

Function of temperature and expressed in form of Cp= a + bT+ cT2 + dT3 . Values of a, b, c and d are given in Table B.2.

Relationship Cp and Cv:

Heat capacity, Cp for a mixture

calculate the total enthalpy change as the sum of the enthalpy changes for pure components.

Cpi = Cp for ith component

yi = mass or moles fraction

)()()( TCyTC piimixp

Change in T at Constant P & Constant Phase

Sensible heat Heat that must be transferred to RAISE or LOWER the temperature of substance or mixture of substance.

We already know that:

Both the specific internal energy and specific enthalpy of substance is strongly dependent on temperature.

UQ HQ

Specific internal energy change:

where Cv- heat capacity at constant volume

Ideal gas : exact

Solid or Liquid : good approx.

Nonideal gas : valid only if V is constant

dTTCU

T

T

v )(

2

1

Specific enthalpy change

where Cp- heat capacity at constant pressure

Ideal gas : exact

Non-ideal gas : exact only if P is constant

Solid & Liquid

2

1)(

T

Tp dTTCH

2

1)(

T

Tp dTTCPVH

Try this

Calculate (kJ/mol) for H2O(v, 30C, 0.0424 bar) H2O(v, 350C, 1 bar)

a. Using the steam tables

b. Using Eq (8.3 10a)

c. Which calculated value is most accurate and why?

Phase changes at constant T & constant P

Usually accompanied by large changes in internal energy and enthalpy.

Latent heat: Specific enthalpy change associated with the phase at constant temperature and pressure.

2 most common latent heata. Solid to Liquid: A (s, Tm, 1 atm) A (l, Tm, 1 atm), =

mwhere

Tm = normal melting point (Table B.1) m = heat of fusion at Tm (Table B.1)

m m (8.4-1)

a. Liquid to Vapor: A (l, Tb, 1 atm) A (v, Tb, 1 atm), = vwhere

Tm = normal boiling point (Table B.1)

m = heat of vaporization at Tb (Table B.1)

v v PV v - RTb (8.4-2)

Procedure Energy Balance Calculations

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.

Open system:

Closed system:

pk EEUWQ

pks EEHWQ

Procedure Energy Balance Calculations-cont.

3. Construct inlet-outlet enthalpy table of each species for close system or open system. Species with few phases are considered a separately.

For closed (open) system, construct a table with columns for initial and final amounts of each species (mior ni) and specific internal energies () [specific enthalpies ()] relative to the chosen reference states.

Procedure Energy Balance Calculations-cont.

4. Choose a reference state phase, temperature, and pressure for each species involved in the process. (Choose the reference state used in the standard table (Table B.8) or choose one either inlet or outlet states as reference state so that at least or can be set to zero.)

Inlet-Outlet Enthalpy Table (Ex. 8.1-1)

References: Ac (l, 20C, 5atm); N2 (g, 25C, 1atm)Substance Inlet Outlet

Ac (v)66.9 3.35

Ac (l)- - 63.55 0

N2 33.1 33.1

inn outninH outH

1H 2H

4H3H

Example of Inlet-Outlet Enthalpy Table

References: Hexane (l, 20C, 5 atm); Benzene (v, 25C, 1 atm)

Substance Inlet Outlet

Hexane (v)n1 n2

Hexane (l)- - n3 0

Benzene (v)n4 0 n5

Benzene (l)n6 n7

inn outninH outH

1H 2H

4H

3H

5H

Constructing an enthalpy table

CONDENSER

0.100 mol H2O (v)/mol0.900 mol D.A./mol110 C, 2 atm

100 mol/s

y (mol H2O(v)/mol satd(1-y) (mol DA/mol)15 C, 1 atm

n2 mol/s

n1 mol H2O (l)/s

15 C, 1 atm

Procedure Energy Balance Calculations-cont.

5. Calculate all required values of or and insert the values in the appropriate places in the table. Then calculate the overall or for the system.

6. Calculate any work, kinetic energy, or potential energy terms ( if you have not dropped from the energy balance).

7. Solve the energy balance,

i

in

ii

out

i HnHnHQ

i

in

ii

out

i UnUnUQ

Calculate the Q required (Ex. 8.4-4)

An equimolar liquid benzene (B) and toluene (T) at 10C and 1 atm is fed continuously to a vessel which the mixture is heated to 50C at constant pressure. The liquid product is 40 mole% benzene and the vapor is 68 mole% benzene. Calculate heat that must be transferred to the mixture.

Calculate the Q required

An equimolar liquid mixture containing benzene and toluene at 20C and 1 atm is fed continuously into a single-stage evaporator. The vapor and liquid phases are separated and discharged as separate streams at 75C at constant pressure. 60% of the benzene fed to the evaporator is recovered as vapor and the liquid product leaves the unit contains 54 wt% toluene. Determine the heat required by the evaporator in kilowatts (kW).