Chapter 7

Energy and Energy Balance

By :Dr Ku Syahidah Ku Ismail

Importance of Energy Calculations

You’ve seen that raw materials and products must be moved into and out of various reactors, mixers, and separators. All these operations involve energy.

Eg. How much power (energy/time) is required to pump 1000 L/h of water from storage vessel to a process unit? (This answer determines the size of the required pump motor.)

Eg. How much coal must be burned each day to produce enough energy to generate the steam to run the turbines to produce enough electricity to meet the daily power requirements of a city of 500,000 people?

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Forms of EnergyThree component of total energy of a system Kinetic energy (Ek)

energy due to the translational motion of the system as a whole relative to some frame of reference (usually the earth’s surface) or to rotation of the system about some axis.

Potential energy (Ep) energy due to the position of the system in a potential

field (such as a gravitational or electromagnetic field). Internal energy (U)

all energy possessed by a system other than kinetic and potential energy; or

Energy due to translation, rotation, vibration & electromagnetic interactions of the molecules, atom and subatomic particle within the system.

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Transfer of Energy In closed system (i.e. no mass is transferred across the

system boundaries while the process is taking place), energy may be transferred between such a system and its surroundings in two ways as heat or work.

Heat Energy that flows as a result of temperature difference

between a system and its surroundings. The direction of flow is always from a higher temperature

to a low one. Heat is defined as positive when its transferred to the

system from the surroundings. Work

energy that flows in response to any driving force other a temperature difference, such as a force, a torque or a voltage

Work is defined as positive when it is done by the system on the surroundings.

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First Law of ThermodynamicsLaw of conservation of energy, which state that energy can neither be created nor destroyed.

General form of first law of thermodynamics

Inlet Energy + Heat - Outlet Energy – Work = Accumulation

Inlet energy and outlet energy is summation/total of all energy such as potential, kinetic and internal energy

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Kinetic Energy Equation (Ek) Kinetic energy, Ek (J) of an object of mass m (kg) moving

with velocity u (m/s) relative to the surface of the earth is

If the fluid enters a system with a mass flow rate (kg/s) and uniform velocity u (m/s), the rate at which kinetic energy (J/s) is transported into the system is

2

2

1muEk

2

2

1umEk

kE

m

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Potential Energy Equation (Ep)

Gravitational potential energy, Ep

if the fluid enters a system with a mass flow rate (kg/s) and an elevation z relative to the potential energy reference plane.

Normally we are interested in the change of potential energy during energy balance calculation

mgzE p

m

gzmE p

)( 1212zzgmEEE ppp

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Example 7.2-1Water flows into a process unit through a 2 cm ID pipe at a rate of 2 m3/h. Calculate the kinetic energy transport in this stream in unit J/s.

Solution:

Ek= 0.870 N.m/s= 0.870 J/s

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Class Discussion

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Energy Balances on Closed System

Closed system no mass is transferred across the system boundaries

while the process is taking place Energy balance

Final System Energy – Initial System Energy = Net Energy Transferred to the System

Initial energy system = Ui + Eki + Epi

Final energy system = Uf + Ekf + Epf

Net energy transfer = Q-W

(Uf-Ui) + (Ekf-Eki) + (Epf-Epi) = Q-W

WQEEU pk

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Energy Balances on Closed System

When applying energy balance equation to a given process, you should be aware of the following points;

1. The internal energy of a system depends almost entirely on the chemical composition, state of aggregation (solid, liquid, or gas), and temperature of the system materials. If no temperature changes, phase changes, or chemical reactions occur in a closed system and if pressure changes are less than a few atmospheres, then ∆U ≈ 0.

2. If a system is not accelerating, then ∆Ek = 0. If a system is not rising or falling, then ∆Ep = 0.

3. If a system and its surroundings are at the same temperature or the system is perfectly insulated, then Q = 0. The process is then termed adiabatic.

4. Work done on or by a closed system is accomplished by movement of the system boundary against a resisting force or the passage of an electrical current or radiation across the system boundary. If there are no moving parts or electrical current at the system boundary, then W = 0.

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Class DiscussionExample

7.3-1

Example 7.3-1

A gas is contained in a cylinder fitted with a movable piston. The initial gas temperature is 25C. The cylinder is placed in boiling water with the piston held in a fixed position. Heat in the amount of 2 kcal is transferred to the gas, which equilibrates at 100C.

The piston is then released, and the gas does 100 J of work in moving the piston to its new equilibrium position. The final gas temperature is 100C.

Write the energy balance equation. Solve the unknown energy term. Express energy in Joules.

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Energy Balances on Open System

In open system, mass is transferred across the system boundaries while the process is taking place.

Therefore work must be done on open system to push mass in and work is done on the surrounding by mass that emerges from the systems.

Both work terms must be include in the energy balance for open system

The net work done by an open system

and

- shaft work rate of work done by the process fluid on a moving part within the system such as a pump rotor.

- flow workrate of work done by the fluid at the system outlet

minus rate of work done by the fluid at the system inlet.

fls WWW ininoutoutinoutfl VPVPWWW

sW

flW

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Energy Balances on Open System

^ symbol is used to denote the specific property (property divided by mass or by mole) such as specific internal energy (Û kJ/kg), specific volume ( m3/kg) and so on.

One important property for energy balance on open system is specific enthalpy (Ĥ kJ/kg).

Sometimes, universal gas law constant can be used as a conversion factor to evaluate specific enthalpy.

V̂

VPUH ˆˆˆ

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Class DiscussionExample

7.4-1

Example 7.4-1

The specific internal energy of helium at 300K, 1 atm is 3800 J/mol.

The specific molar volume, 300 K, 1 atm is 24.63 L/mol.

Calculate: Specific enthalpy of helium at 300K, 1 atm The rate at which the enthalpy is

transported by a stream of helium at 300K, 1 atm with a molar flowrate of 250 kmol/h.

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Energy Balances Equation for Open System

spk WQEEH

streaminput

jj

streamoutput

jj

streaminput

jj

streamoutput

jjk

streaminput

jj

streamoutput

jj

gzmgzmpE

umumE

HmHmH

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ˆˆ

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Class DiscussionExample

7.4-2

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Reference States and State Properties

It is not possible to know the absolute value of Û and Ĥ for a process material, but we can determine the change in ΔÛ and change in ΔĤ corresponding to a specific change of state (temperature, pressure, phase).

A convenient way to tabulate ΔÛ and ΔĤ is to choose a temperature, pressure and state of aggregation (i.e. phase) as a reference state.

Since Ĥ cannot be known absolute, for convenience we may assign a value Ĥo=0 to be reference state. Then ΔĤ1= Ĥ1-0; ΔĤ2= Ĥ2-0 and so on.

Some enthalpy tables give the reference states on which the listed values of Ĥ are based and others do not.

However, we do not have to know the reference state to calculate ΔĤ for the transition from one state to another state since the value are based on the same reference in the table.

Ĥ and Û can be said as state properties Property whose change of value in any process depend only on it

initial and final states and do not depend on the path take to reach the state.

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Class DiscussionExample

7.5-1

Phase Diagram for Water

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Steam Table

Class DiscussionExample

7.5-2

Example 7.5.2

1. Determine the vapor pressure, specific internal energy, and specific enthalpy of saturated steam at 133.5C.

Show that water at 400C and 10 bar is superheated steam and determine its specific volume, specific internal energy and specific enthalpy relative to liquid water at the triple point, and its dew point.

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Class DiscussionExample

7.5-3

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Energy Balance Tips When labeling flowchart, write down together the

temperature, pressure and state of aggregation of the process material eg. H2O(s) or H2O(v)

Normally (depend on the process description) for chemical process unit; shaft work, kinetic and potential energy change tend to be negligible compared to heat flows, internal energy and enthalpy changes.

Then simplified energy balance become

Closed System:

Open System:

UQ

HQ

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Class DiscussionExample

7.6-1

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Class DiscussionExample

7.6-3

Simultaneous Material and Energy Balance

Saturated steam at 1 atm is discharged from a turbine at a rate of 1150 kg/h. Superheated steam at 300C and 1 atm is needed as a feed to a heat exchanger; to produce it, the turbine discharge stream is mixed with superheated steam available from a second source at 400C and 1 atm. The mixing unit operates adiabatically. Calculate the amount of superheated steam at 300C produced and the required volumetric flow rate of the 400C steam.

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Mechanical Energy Balance Important in the operations involve the flow of fluids to,

from and between tanks, reservoirs and process unit. Mechanical energy balance for steady state flow of an

incompressible fluid; where F is friction loss

Bernoulli equation Simplified mechanical energy balance for frictionless

process (F=0) in which no shaft work is performed (Ws=0).

m

WFzg

uP s

ˆ2

2

02

2

zguP

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Class DiscussionExample

7.7-1

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Class DiscussionExample

7.7-2

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Class DiscussionExample

7.7-3