Energy Balance

S.Gunabalan Associate Professor Mechanical Engineering Department Bharathiyar College of Engineering & Technology Karaikal - 609 609. e-Mail : gunabalans@yahoo.com

Part - 2

Energy accounting

• Energy accounting is a system used to measure, analyze and report the energy consumption of different activities on a regular basis.

• It is done to improve energy efficiency

Energy Balances

Energy Balances is the law of conservation of energy, Unit II 13) Discuss briefly the energy balance for closed and open system (Nov 2011) OR explain or derive energy balance equation OR Explain or derive Steady Flow Energy equation

Energy Balances on Closed Systems • Example for a Closed System

– Storage tank ΔU + ΔEk + ΔEp = Q - W

K – kinetic energy P- Potential energy • ΔU = 0 if there are no temperature changes, phase changes, or

chemical reactions. ΔEk = 0 if the system doesn't accelerate

• ΔEp = 0 if the system doesn't change in height • Q = 0 if the system doesn't exchange heat with the surroundings,

that is, if the system is adiabatic or insulated • W = 0 if the system has no moving boundry (ex. piston), or if there

are no moving parts, electrical current, or radiation exchange with the system and the surroundings.

Thermodynamic System

Thermodynamic System Open system

http://chemwiki.ucdavis.edu/Physical_Chemistry/Thermodynamics/A_System_And_Its_Surroundings

A open system is defined when a fixed volume is under study. There can be mass transfers as well as energy transfers across the boundary.

Thermodynamic System

• Truly isolated systems cannot exist in nature, • The only possibility is the universe itself, • So its is a hypothetical concepts

http://chemwiki.ucdavis.edu/Physical_Chemistry/Thermodynamics/A_System_And_Its_Surroundings

isolated systems

Thermodynamic System

http://chemwiki.ucdavis.edu/Physical_Chemistry/Thermodynamics/A_System_And_Its_Surroundings

Closed systems

• A closed system is a system that exchanges only energy with its surroundings, not matter.

• Matter can no longer transfer because the lid prevents matter from entering the pan and leaving the pan. Still, the pan allows energy transfer.

A closed system always contains the same matter. There can be no mass transfers across the boundary. There may be energy transfer across the boundary.

First law of thermodynamics

푑푄 = 푑푊

푄 = 푈푇표푡푎푙 + 푊푇표푡푎푙 푈푇표푡푎푙 = 푄 + 푊푇표푡푎푙

∆푢 + ∆퐸푘푖푛푒푡푖푐 + ∆퐸푝표푡푒푛푡푖푎푙 = 푄 − (푊푠ℎ푎푓푡 + 푊푓푙표푤)

∆퐻 = ∆푢 + 푊푓푙표푤

(∆푢 + 푊푓푙표푤) + ∆퐸푘푖푛푒푡푖푐 + ∆퐸푝표푡푒푛푡푖푎푙 = 푄 − (푊푠ℎ푎푓푡)

∆퐻 + ∆퐸푘푖푛푒푡푖푐 + ∆퐸푝표푡푒푛푡푖푎푙 = 푄 −푊푠ℎ푎푓푡

Energy Balances on Open Systems

∆퐻 + ∆퐸푘푖푛푒푡푖푐 + ∆퐸푝표푡푒푛푡푖푎푙= 푄 −푊푠ℎ푎푓푡

(퐻2 − 퐻1) + 퐸푘2 − 퐸푘1 + (퐸푝2 − 퐸푝1) = 푄 −푊푠ℎ푎푓푡

퐻1 + 퐸푘1 +퐸푝1 +

푄 = 퐻2 + 퐸푘2 + 퐸푝2 + 푊푠ℎ푎푓푡

Energy Balances on Open Systems

퐸푘푖푛푒푡푖푐 = 12푚푉

퐸푝표푡푒푛푡푖푎푙 = mgH m – mass, g – gravity,

H – Height or height from datum (z) We better use z instead of H

퐸푝표푡푒푛푡푖푎푙 = mgz

Energy Balances on Open Systems

퐻1 +12푚푉1

2 + 푚푔푧1 + 푄 = 퐻2 +12푚푉2

2 + 푚푔푧2 + 푊

Convert in to specific term ie /Kg

ℎ1 +12푉1

2 + 푔푧1 +푑푄푑푚

= ℎ2 +12푉2

2 + 푔푧2 +푑푤푑푚

Energy Balances on Open Systems

퐸nergy transfer per unit mas ( )

Work transfer per unit mas ( )

ℎ1 + 푉1 2 + 푔푧1 +푑푄푑푚 = ℎ2 + 푉2 2 + 푔푧2 +

푑푊푑푚

Steady Flow Energy equation

Energy Balances on Open Systems

Also Called

푽 is Velocity

This equation based on mass flow rate 풅풎

ℎ1 + 푉1 2 + 푔푧1 +푑푄푑푚 = ℎ2 + 푉2 2 + 푔푧2 +

푑푊푑푚

X by 풅풎풅풕푖푠푐푎푙푙푒푑푚푎푠푠푓푙표푤푟푎푡푒 푤 푢푛푖푡

풅풎풅풕

(ℎ1 + + 푔푧1) + 풅풎풅풕

= 풅풎풅풕

(ℎ2 + + 푔푧2) + 풅풎풅풕

풅풎풅풕

represented as w

풘(ℎ1 + 푉1 2 + 푔푧1) +푑푄푑푡

= 풘(ℎ2 + 푉2 2 + 푔푧2) +푑푊푑푡

Energy Balances on Open Systems 푽 is Velocity

Derive the steady flow energy equation for open system on time basis (Apr/May 2010)

This equation based on Time 풅풕

Mass Balance

• Conservation of mass – The mass flow rate of a system at entry equal to

mass flow rate at exit of the system 푤푖푛푙푒푡 = 푤표푢푡푙푒푡

퐴1푽1

푣1= 퐴2푽2

푣2

This is Equation of Continuity 푽 – Velocity of flow

푽

= //

=

= mass flow rate

Steady Flow systems

• Steady Flow systems where mass flow in equals mass flow out.

• In unsteady flow systems parameters such as pressure, mass, temperature etc. will

• change with time. (hence ‘unsteady’) • In steady flow systems parameters such as

pressure, mass, temperature etc. will remain • constant with time. (hence ‘steady’

Reference • Rajput, R. K. 2010. Engineering thermodynamics. Jones and Bartlett

Publishers, Sudbury, Mass. • Nag, P. K. 2002. Basic and applied thermodynamics. Tata McGraw-Hill, New

Delhi. • http://blowers.chee.arizona.edu/201project/EBopensys.pg1.HTML • http://chemwiki.ucdavis.edu/Physical_Chemistry/Thermodynamics/A_Sys

tem_And_Its_Surroundings