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Basics of Energy and Heat Transfer

Objectives:

• Heat and other forms of energy• Heat capacity• Thermodynamic and heat transfer• Energy balance

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Forms of energy

The total energy of a system that can be stored has three components, kinetic energy, potential energy, and internal energy:1. Kinetic Energy (Ek): is energy a system, or some material has because of its velocity relative to the

surroundings.

JmNsmkg

N

s

mkg

mvEk

22

22

/2

kg

mN

smkg

N

s

mvEk

22

22

/2ˆ

hr

J

hr

mN

smkg

N

s

m

hr

kgvmEk

22

22

/2

2. Potential energy (Ep): is energy a system has because of the force exerted on its mass by a gravitational field with respect to a reference surface.

JmNsmkg

N

s

mkgmghEp

22

2

/

Energy per unit time

Energy per unit mass

kg

mN

smkg

N

s

mghE p

22

2

/Energy per unit mass

hr

J

hr

mN

smkg

N

s

m

hr

kgghmE p

22

2

/Energy per unit time

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Example: Kinetic energy and potential energy

1. Water flows into a process unit through a 2-cm inner diameter(ID) pipe at a rate of 2 m3/hr. Calculate Ek̊ for this stream (J/s).

2. Crude oil is pumped at a rate of 15.0 kg/s from a well 220 m deep to a storage tank 20 m above ground level. Calculate the rate at which potential energy increases (J/s).

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Forms of Energy cont’d

3. Internal Energy (U) :All energy possessed by system other than kinetic and potential energy, including the energy due to the:– rotational and vibration motion of molecules within the system– interactions between molecules within the system– motion and interactions of electrons and nuclei within molecules

For a single phase and single component, Specific Internal Energy is function of T and V: Û = Û(T,V)

By definition:

DÛ can be calculated using DÛ = ∫Cv(T)dT

where Cv is the heat capacity at constant volume.

CV defined to be the amount of heat necessary to raise the temperature of one kilogram of substance by one degree in a closed system.

Vd

V

UdT

T

UUd

TV

V

V

ctyheatcapaciT

U

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Enthalpy (Ĥ)

It is not possible to know the absolute value of Û or Ĥ for a pure substance, but you can determine thechange in Û(DÛ) or Ĥ(DĤ) corresponding to a specified change of state (temperature, pressure, andphase).

A common practice is to arbitrarily designate a reference state for a substance at which Û and Ĥ aredeclared to be equal to zero, and then tabulate and/or for the substance relative to the reference state.

For example,CO (g, 0°C, 1 atm) → CO (g,100°C, 1 atm): DĤCO=2919 J/s

DĤCO = ĤCO-0=2919 J/molreference state

We say: “the specific enthalpy of CO at 100°C and 1 atm relative to CO at 0°C and 1 atm is 2919 J/mol”.

dP

P

HdT

T

HHd

TP

VpUH , where p is absolute pressure and V is specific volume. For a single phase and single component, Specific enthalpy is function of T and p: Ĥ = Ĥ (T,p)

DĤ can be calculated using DĤ = ∫Cp(T)dTWhere Cp is the heat capacity at constant pressure.

^

p

p

ctyheatcapaciT

H

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Example: Calculation of an internal energy change and enthalpy

What is the change in internal energy when 10 kg mol of air is cooled from 60 ̊C to 30 ̊C in a constant volume process? Calculate the enthalpy change for the same process except assume that the enthalpy change occurs in a constant pressure.

Cv=2.1× 104 J/(kg mol)( ̊C)

∆U= 10 kg mol =2.1×105(30-60)=-6.3 ×106 J

Cp=2.1× 104 J/(kg mol)( ̊C)

∆H= 10 kg mol =2.9×105(30-60)=-8.7 ×106 J

DU= m ∫Cv(T)dT

DH = m ∫Cp(T)dT

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Transfer of energy

In a closed system (no mass transferred across the system boundaries (i.e., batch system)),energy can still be transferred between the system and the surroundings in two ways:

1. Heat (Q) – energy that flows due to a temperature difference between the system andits surroundings. Heat transfer is usually classified in three categories: Conduction,Convection, and Radiation. Heat is defined to be positive if it flows to a system (i.e.input).

2. Work (W) – is a form of energy that represents a transfer of energy between the systemand surroundings due to any driving force such as mechanical force, shaft work. Work isdefined as positive when the surroundings perform work on the system.

A system does not possess heat or work. Heat or work only refer to energy that is beingtransferred to the system.

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Thermodynamics and Heat Transfer

Heat is a form of energy that can be transferred from one system to another as a result of temperature difference.

We are normally interested in how long it takes for the hot coffee in athermos to cool to a certain temperature, which cannot be determined froma thermodynamic analysis alone.

• Thermodynamics deals with equilibrium states.• Heat transfer deals with nonequilibrium states.

First law of thermodynamics:Rate of energy transfer into a system = rate of increase of the energy of the system

Second law of thermodynamics:Heat is transferred in the direction of decreasing temperature

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Temperature difference is the driving force for heat transfer.• Voltage difference is the driving force for electric current flow.• Pressure difference is the driving force for fluid flow.• The rate of heat transfer in a certain direction depends on the magnitude of the temperature gradient in that direction.• Temperature gradient: rate of change of temperature.

Application Areas of Heat Transfer

What is the Driving Force for Heat Transfer?

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Units of energy

Energy has units of force times distance (mass.length2/time2)

SI: N.m (Joule) AE: ft.lbf (Btu)

A calorie is defined in terms of the amount of heat required to raise the temperature of one mLof water by one degree Centigrade.

Unit Symbol Mass of H2O Temperature Interval

kilocalorie kcal 1 kg °Ccalorie cal 1 g °CBritish thermal unit Btu 1 lbm °F

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First Law of Thermodynamics ( Energy balance)

The First Law of Thermodynamics states that energy can neither be created or destroyed(just like total mass)

Accumulation = In – Out + Generation – Consumption

But generation=0 and consumption=0 since energy cannot be created or destroyed so the general balance becomes:

Accumulation = In – Out

minput(Uinput+Ekinout+Epinput ) moutput(Uoutput+Ekoutput+Epoutput )System energy (U+PE+KE)=E

(E may change with time, ∆E)

Surroundings may do work on the system, W

Heat, Q, may enter the system

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Energy balances on closed systems

Closed System – no material crosses the system boundary over a period of time (e.g., batch process).

General balance equation is: Accumulation = Input – Output

Although no mass crosses the boundaries, energy input≠0 and energy output≠0 since energy can be transferred across the boundary, Therefore, the balance becomes:

final system energy –initial system energy = net energy transferred

Initial system energy = Ui+Eki+Epi

Final system energy = Uf+Ekf+Epf

Net energy transferred= Q+W

∆E= ∆U+ ∆Ek+ ∆Ep =Q+W

1st Law of Thermodynamicsfor a closed system(Δ = final – initial)

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Notes on energy balances for a closed system

∆E=∆U+ ∆Ek+ ∆Ep =Q+W

Possible Simplifications:

if Tsystem = Tsurroundings, then Q = 0 since no heat is being transferred due to temperature difference.

if the system is perfectly insulated, then Q = 0 (system is adiabatic) since no heat is being transferred between the system and the surroundings.

if system is not accelerating, then ΔEk = 0

if system is not rising or falling, then ΔEp= 0

if energy is not transferred across the system boundary by a moving part (e.g., piston, impeller, rotor), then W = 0

if system is at constant temperature (system is isothermal), no phase changes or chemical reactions are taking place, and only minimal pressure changes, then ΔU = 0

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Examples of closed systems

Example 1: Heating water in a sealed container

Example 2: Compressing a gasin a cylinder.

+ +

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Example: Closed systems

Write and simplify the closed-system energy balance for each of the following processes.(a) The contents of a closed flask are heated from 25°C to 80°C.

(b) A chemical reaction takes place in a closed adiabatic (perfectly insulated) rigid container.