• Energy itsself is often designed as the capacity to do work or transfer heat, a fuzzy concept.
• It is easier to understand specific types of energy.
• Energy is not some sort of invisible fluid.
• Energy is not something that can be measured directly.
Concepts of Energy
TYPES OF ENERGY
A. Energy transfer between the system and surroundings without any accompanying mass transfer OR ENERGY THAT can not be stored in a system-they are solely transfer into and out of a system.
1. Work
Mechanical work Electrical work Shaft work
Flow work (chapter 22).
2. Heat
B. Energy that can be stored, that is, retained because material has associated energy: kinetic, potential and internal energy.
3. kinetic, 4. potential
5. internal energy
Work is a path function, and the value depends on the initial state, the path, and the final state of the system.
Mechanical work : work that occurs because of a mechanical force that moves the boundary of a system.
State 1 State 2
F
Electrical work : electrical work occurs when am electrical current passes through an electrical resistance in the circuit.
Shaft work : shaft work occurs by a force acting on a shaft to turn it against mechanical resistance.
Flow work : flow work is performed on the system when fluid is pushed into the system by the surrounding occurs by a force acting on a shaft to turn it against mechanical resistance.
Heat is commonly defined as that part of the total energy flow
across a system boundary that caused by a temperature difference (potential) between the system and the surrounding (or between two systems).
Heat is a path function.
• Kinetic energy (EK) is the energy a system, or some material,
possesses because of its velocity relative to the surroundings, which are usually, but not always, at rest.
• The kinetic energy of a material refers to what is called the
macroscopic kinetic energy, namely the energy that is associated with the gross movement (velocity) of the system or material, and not the kinetic energy of the individual molecules that belong in the category of internal energy.
• The value of a change in te specific kinetic energy ( ) occurs in a specified time interval, and depends only on the initial and final
values of the mass and velocity of the material.
KE
• Potential energy (PE) is energy the system possesses because of the force exerted on its mass by a gravitational or electromagnetic field with respect to a reference surface.
• The value of a change in the specific potential energy, , occurs in a specified time interval, and depends only on the initial and final states of the system (state variabel), and not on the path followed.
PE
• Internal energy (U) is macroscopic concept that takes into account all of the molecular, atomic, and subatomic energies, all of which follow definite microscopic conservation rules for dynamic system.
Internal energy can be stored. Because no instruments exist with which to measure internal energy directly on a macroscopic scale, internal energy must be calculated from certain other variables that can be measured microscopically, such as pressure, volume,
temperature, and composition.
• To calculate the internal energy per unit mass ( ) from the
variables that can be measured, we make use of a special property of internal energy, namely that it is an exact differential because it is a point or state variable.
U
• Custom dictates the use of temperature and specific volume as the two variables. For a single phase and single component, we say that is a function of T and
By taking the total derivative, we find that
(21.5) By defiinition is the “heat capacity” (specific heat) at constant volume, given the special symbol Cv.
U
V
ˆ) , ˆ(
ˆ U T V
U =
V V d
dT U T
U U d
T V
ˆ ˆ ˆ ˆ ˆ
ˆ
+
=
(
Uˆ /T)
Vˆ• For all practical purpose in this text, the term is so small that the second term on the righthand side of Equation (21.5) can be neglected. Consequently, changes in the specified intenal energy over a specified time interval can be computed by integrating
Equation (21.5) as follows:
(21.6)
For an ideal gas U is a function of temperature only. Equation (21.6) alone is not valid if a phase change occurs during the processs.
• Note that you can only calculate differences in internal energy, or calculate the internal energy relative to a reference state, but not absolute values of internal energy.
(
Uˆ /Vˆ)
T
==
−
=
2
1 2
1
ˆ 1 ˆ
2 ˆ ˆ
ˆ
ˆ T
T
v U
U
dT C
U d U
U U
• The principles of the conservation of energy states that the total energy of the system plus the surroundings can neither be created nor destroyed*
*Can mass be converted into energy according to E=mc2? It is not correct to say that E=mc2 means mass is converted into energy. The equal sign can mean that two quantities have the same value as in measurements of two masses in an experiment, or it may mean (as in general relativity) that the two variables are the same or are
equivalent things. It is in the latter sense that E=mc2 applies, and not in terns of converting a rest mass into energy. You might write ΔE=c2Δm. If Δm is negative, ΔE is also negative. What this means is as the inertia mass decreases, ΔE decreases, and the reverse.
The Concept of the Conservation of Energy
Energy Balances for Closed Systems
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
Unsteady state Systems
(U+PE+KE)inside = E = Q + W
Steady state Systems 0 = Q + W
All work done on a closed, steady state system must be transferred out as heat.
However, Heat added to a closed, steady state system Q does not always equal the work done by the system (-W). (second law of thermodynamics).
Energy Balances for Open Systems
P1
P2
E = ([U1 + P1V1] + Ek1 + Ep1) - ([U2 + P2V2] + Ek2 + Ep2) + Q - Ws
E = (H1 + Ek1 + Ep1) – (H2 + Ek2 + Ep2) + Q - Ws
Unsteady state Systems : E 0 Steady state Systems : E = 0
• The accumulation term (ΔE) in the energy balance can be nonzero because:
1. the mass in the system changes
2. the energy per unit mass in the system changes, and
3. both 1 and 2 occur.
Accumulation term (inside the system)
Type of energy in the system At time t1 At time t2
Internal Ut1 Ut2
Kinetic KEt1
Et1 KEt2
Et2
Potential PEt1 PEt2
Mass of the system mt1 mt2
Energy accompanying mass transport (through the system boundary) during the interval t1to t2
Type of energy Transport in Transport out
Internal U1 U2
Kinetic KE1 KE2
Potential PE1 PE2
Mass of the flow m1 m2
Net heat exchange between the system and the surroundings during the interval t1to t2
Q
Works terms (exchange with the
surroundings) during the interval t1to t2
Wshaft Net shaft, mechanical, and electrical work W Wmechanical
Welectrical Flow work done on the system to introduce
material into the system
Flow work done on the surroundings to remove material from the system
ˆ ) ( 1 1
1 pV m
ˆ ) ( 2 2
2 p V
−m
TABLE 22.1 Summary of the Symbols to be Used in the General Energy balance
• The represent the so-called “pV work,” “pressure energy,” “flow work,” or “flow energy,” that is, the work done by the surroundings to put a mass of
matter into the system at boundary 1, and the work done by the system on the surroundings as a unit mass leaves th esystem at boundary 2, respectively.
Because the pressures at the entrance and exit to the system are deemed to be constant for differential
displacement of mass, the work done per unit mass by the surroundings on the system adds energy to the system at boundary 1:
1 1 1
1 ˆ
0 1
1 ˆ ( ˆ 0) ˆ
ˆ 1 p dV p V p V
W
V
=
−
=
=
Enthalpy
• We will axpress the enthalpy in terms of the temperature and pressure (a more convenient variable) than the specific volume).
(21.10)
By definition is the heat capacity at constant pressure, and is given the special symbol Cp. For most practical purposes is so small at modest pressure that the second term on the righthand side of Equation (21.10) can be neglected.
However, in processes operating at high pressure, the second term on the righthand side of Equation (21.10) cannot necessarily be
neglected, but must be evaluated from experimental data.
) , ˆ (
ˆ H T p
H =
p dp dT H
T H H
d
T p
+
= ˆ ˆ
ˆ
(
Hˆ /T)
p(
Hˆ /p)
Tන
𝐻𝑅𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝐻
𝑑𝐻 = න
𝑇𝑅𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑇
𝐶𝑝 𝑇 𝑑𝑇
Reference States and State Properties
H is a state property, or a property of a system component whose value
depends only on the state of the system (temperature, pressure, phase, and composition) and not on how the system reached that state.
Since H cannot be known absolutely, for convenience we may assign a value HReference = 0 to the reference state.
Felder & Rousseau (Example 8.3.5) Energy Balance on a Gas Preheater
A stream containing 10% CH4 and 90% air by volume is to be heated from 20 °C to 300 °C. Calculate the required rate of heat input in kilowatts if the flow rate of the gas is 2.00 X 103 liters (STP)/min.
Q
2000 L (STP)/min, 20 oC 0.1 CH4
0.9 Air
300 oC 0.1 CH4 0.9 Air
22.4 L (STP) = 1 mol
Table B.2 Heat Capacities (Felder & Rousseau)
No. Component a b c d
1 CH4 3.43E-02 5.47E-05 3.66E-09 -1.10E-11 2 Air 2.89E-02 4.15E-06 3.19E-09 -1.97E-12
Cp [kJ/(mol.oC)] (gas) a+bT+cT2+dT3
<1> <2>
TRef. = 20oC
22.4 L (STP) = 1 mol 2000 L (STP) = 89.29 mol
T = 20 T = 300
Q
No. Component a b c d mol frac. mol energy mol frac. mol energy
1 CH4 3.43E-02 5.47E-05 3.66E-09 -1.10E-11 0.1 8.93 0.00 0.1 8.93 107.75
2 Air 2.89E-02 4.15E-06 3.19E-09 -1.97E-12 0.9 80.36 0.00 0.9 80.36 668.07
total 1.0 89.29 0.00 1.0 89.29 775.81 775.81
Q = 12.93 kW
Cp [kJ/(mol.oC)] (gas) a+bT+cT2+dT3
<1> <2>
Felder & Rousseau (Example 8.3.6) Energy Balance on a Waste Heat Boiler
A gas stream containing 8.0 mole% CO and 92.0 mole% CO2 at 500°C is fed to a waste heat boiler, a large metal shell containing a bundle of small-diameter tubes. The hot gas flows over the outside of the tubes. Liquid water at 25°C is fed to the boiler in a ratio 0.200 mol feedwater/mol hot gas and flows inside the tubes. Heat is transferred from the hot gas through the tube walls to the water, causing the gas to cool and the water to heat to its boiling point and evaporate to form saturated steam at 5.0 bar. The steam may be used for heating or power generation in the plant or as the feed to another process unit. The gas leaving the boiler is flared (burned) and discharged to the
atmosphere. The boiler operates adiabatically-all the heat transferred from the gas goes into the water, as opposed to some of it leaking through the outside boiler wall. The
flowchart for an assumed basis of 1.00 mol feed gas is shown below. What is the temperature of the exiting gas?
<1> 1 mole, 500°C 8 % CO
92% CO2
<2> 1 mole, ? °C
<3> 0.2 mole
H2O (liquid, 25 °C) H2O (vapor, 5 Bar,
saturated)
<4> 0.2 mole
TReference = 0.01 oC (liquid, triple point)
H2O (vapor, 5 Bar, saturated, 151.8 oC), H = 2747.5 kJ/kg = 49455 J/mol
H2O (liquid, 25 °C), H = 104.8 kJ/kg = 1886.4 J/mol
TRef. = 0.01oC
H = 1.8864 kJ/mol H = 49.46 kJ/mol
T = 500 T = 297.2649 T = 25 T = 151.8
No. Component a b c d mol frac. mol energy mol frac. mol energy mol frac. mol energy mol frac. mol energy
1 CO 2.90E-02 4.11E-06 3.55E-09 -2.22E-12 0.08 0.08 1.21 0.08 0.08 0.71 0 0 0 0 0 0
2 CO2 3.61E-02 4.23E-05 -2.89E-08 7.46E-12 0.92 0.92 20.37 0.92 0.92 11.36 0 0 0 0 0 0
3 H2O 0 0 0 0.00 0 0 1 0.2 0.37728 1 0.2 9.891
total 1.00 1 21.58 1.00 1 12.07 1 0.2 0.37728 1 0.2 9.891
12.07 0.00001
<4>
a+bT+cT2+dT3
Cp [kJ/(mol.oC)] (gas) <1> <2> <3>
degrees of freedom analysis for energy balance with reaction
degrees of freedom = number of unknowns –
number of independent equations ND = NU – NE
NU = NS + NR + NQ + NW - NK; NS = number of streams NR = number of reactions
NQ = number of heat transfers
NW = number of work transfers NK = number of knowns
NE involves only energy balance along with other equations.
