ENERGY AND ENERGY BALANCES

I. Introduction

System – anything in the universe under consideration Types of system

1. Open system – exchange of mass and energy (for continuous process)

2. Closed system – exchange of energy only (for batch process)

3. Isolated system – no exchange of mass nor energy

Energy possessed by the system1. Kinetic energy – due to the translational

motion of the system as a whole relative to some frame of reference or rotation of the system about some axis.

2. Potential energy – due to the position of the system in a potential field (gravitational or electromagnetic field).

3. Internal energy – all other energy possessed other than kinetic and potential such as due to the motion of the molecules, due to rotational or vibrational motions, etc.

Surroundings – anything aside from the system How is energy transferred?

1. Heat – energy that flows as a result of temperature difference

2. Work – energy that flows in response to any driving force other than temperature difference such as a force, a torque, or a voltage.

Signs are arbitrarily assigned as long as it is used consistently.

II. First Law of Thermodynamics

For closed system Accumulation = Input – Output

U + Ek + Ep = Q - W

For open system Input = Output

III. Specific properties and Enthalpy

Extensive property – proportional to the quantity of material (mass, volume, flow rates, kinetic energy, potential energy, internal energy)Intensive property – independent of the quantity (temperature, pressure, density)Specific property – an intensive quantity obtained by dividing an extensive property (or its flow rate) by the total amount (or flow rate) of the process material. The symbol is used to denote a specific property.

Specific volume (V) – volume of a substance / its mass (e.g. cm3/g)

Specific internal energy (U) – kinetic energy of a material / its mass (e.g. J/kg)

Specific enthalpy – a property that occur in the energy balance equation for open system that is defined as:

H = U + PV

IV. Non-reactive process

Changes in pressure at constant temperature

Changes in temperature

Sensible heat - heat that must be transferred to raise or lower the temperature of a substance or mixture of substances.

For closed system : Q = UFor open system : Q = H

H + Ek + Ep = Q - W

U 0 and H [=U + (PV)] VP

Heat capacity – the energy needed to raise the temperature of a substance by one degree. Denoted by Cv or Cp. For constant volume

U Cv(T) dT For constant pressure

H VP + Cp(T) dT Cp can be calculated using Table B.2 of

Appendix B Cv = Cp for solids and liquids; Cv = Cp - R for

ideal gases Can also be calculated using specific enthalpies

H nH H can be obtained from Table B.8 of Appendix

B For solids and liquids: can be estimated using

Kopp’s rule

Changes in Phase

Latent heat – enthalpy change associated with the transition of a substance from one phase to another at constant temperature and pressure.

ExampleLatent heat of vaporization of water = 40.6

kJ/mol (100oC and 1 atm)H2O(l) at 100oC H2O(g) at 100oC

Estimation and correlation:1. Trouton’s rule2. Chen’s equation3. Clapeyron equation4. Watson’s correlation

V. Reactive process

Heat of reaction/Enthalpy of reaction (HR) – the enthalpy change for a process in which stoichiometric quantities of reactants at temperature T and pressure P react completely in

a single reaction to form products at the same temperature and pressure. Important terms and observations:

1. If HR is positive the reaction is endothermic and if HR is negative the reaction is exothermic.

2. At low and moderate pressure, HR is nearly independent of pressure.

3. The value of HR depends on how the stoichiometric equation is written.

4. The value of HR depends on the states of aggregation (gas, liquid, or solid) of the reactant and products.

5. The standard heat of reaction (HRo) is when

both the reactants and products are at a specified temperature and pressure, usually 25oC and 1 atm.

VI. Energy balance on reactive process

Heat of reaction method1. Complete the material balance calculations on

the reactor to greatest extent possible.2. Choose reference states for specific enthalpy

calculations.3. For a single reaction in a continuous process,

calculate the extent of reaction, .4. Prepare the inlet-outlet enthalpy table, inserting

known molar amounts for all inlet and outlet steam components.

5. Calculate each unknown stream component enthalpy, H, as H for the species going from its reference state to the process state, and insert the enthalpies in the table.

6. Calculate H for the reactor.H = HR

o + nout Hout - nin Hin (single reaction)

H = HRo + nout Hout - nin Hin (multiple

reactions)

7. Substitute calculated value of H of the reactor in the energy balance and complete the required calculations.

Heat of formation method

1. Complete the material balance calculations on the reactor to greatest extent possible.

2. Choose reference states for specific enthalpy calculations.

3. Prepare the inlet-outlet enthalpy table, inserting known molar amounts for all inlet and outlet steam components.

4. Calculate each unknown specific enthalpies. H = Hf

o + Hat T

5. Calculate H for the reactor.H = nout Hout - nin Hin

6. Substitute calculated value of H of the reactor in the energy balance and complete the required calculations.

ProblemCalculate the change in enthalpy of the reactor.

Given:

Furnace100 mol C3H8

25oC

600 mol O2

2256 mol N2

300oC

100 mol O2

2256 mol N2

300 mol CO2

400 mol H2O 1000oC

Heating value of fuels

HIGHER HEATING VALUE/TOTAL HEATING VALUE/GROSS HEATING VALUE The negative standard heat of combustion of the fuel

(Hco) with liquid water as a combustion product.

LOWER HEATING VALUE The negative standard heat of combustion of the fuel

based on water vapor as a product.

The relationship between the two:

HHV = LHV + n Hv (H2O, 25oC)where: Hv (H2O, 25oC) = 44.013 kJ/mole

= 18,934 BTU/lbmole

DULONG FORMULA – equation used to estimate heating value of a fuel using the ultimate analysis of the fuel.

HHV(kJ/kg) = 33,801(C) + 144,158[(H) – 0.125(O)] + 9413(S)

Adiabatic flame temperature – The temperature that would be attained if the fuel is burned in an adiabatic combustion chamber and all the energy released went into raising the temperature of the reaction products

The heat losses as well as heat of utilization are equal to zero.

The adiabatic flame temperature increases when pure oxygen instead of air is fed.

The adiabatic flame temperature is greatest when the fuel and oxygen are fed in stoichiometric proportion.

Example:

Liquid methanol is to be burned with 100% excess air. The engineer designing the furnace must calculate the highest temperature that the furnace walls will have to withstand so that an appropriate material of construction can be chosen. Perform this calculation, assuming that the methanol is fed at 25oC and the air enters at 100oC.

Eqn: CH3OH(L) + 3/2 O2(G) CO2(G) + 2H2O(L)

Hco = -726.6 kJ/mol