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Energy Transfer by Heat, Work and Mass. Objectives. • Introduce the concept of energy transfer by heat. • Discuss the various forms of work with emphasis on the moving boundary work. • Discuss the flow work, the work associated with forcing a fluid into or out of a control volume.
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Objectives • Introduce the concept of energy transfer by heat. • Discuss the various forms of work with emphasis on the moving boundary work. • Discuss the flow work, the work associated with forcing a fluid into or out of a control volume. • Discuss the combination of the internal energy and the flow work (i.e. Enthalpy). • Discuss the conservation of mass principle and apply it to various systems. • Show that h+ke+pe represents the energy of a flowing fluid per unit of its mass.
How does energy cross a closed system boundary? • Energy can cross the boundaries of a closed system in the form of heat or work. • If the energy transfer across the boundaries of a closed system is due to a temperature difference, it is heat; otherwise, it is work.
So, what do we mean by Heat? • Heat is defined as the form of energy (thermal energy) that is transferred between two systems (or surroundings) by virtue of a temperature difference. • Heat is energy in transition. It is recognized as it crosses the boundary of a system.
No heat transfer =Adiabatic Process • A process during which there is no heat transfer is called an adiabatic process. • The adiabatic process should not be mixed with Isothermal process. • A process could be an adiabatic process while the temperature of a system is changing .
Symbols of Heat • Q or 1Q2 • Definition: The amount of total heat transferred during a process from state 1 to state 2. • Units: kJ or BTU • q • Heat transfer per unit mass. • Units: kJ/kg or BTU/lbm • Rate of heat transfer • kJ/sec = kW
Sign convention • Heat transferred to a system is positive. • Heat transferred from a system is negative.
What do we mean by Work? • Work is defined as the energy transfer associated with force acting through a distance.
Symbols of Work • W or 1W2 • The amount of work done by or on a system during a process from state 1 to state 2. • Units: kJ or BTU • w • Work per unit mass. • Units: kJ/kg or BTU/lbm • Power: The work done by unit time. • kJ/sec = kW
Sign convention • Work done on a system by an external force acting in the direction of motion is negative. • Work done by a system against an external force acting in the opposite direction of the motion is positive.
Characteristics of Heat and Work • Both of them are boundary phenomena. That is they are recognized at the boundaries of a system as they cross them. • Systems possess energy, not heat or work. • Both are associated with a process, not a state. • Both are path functions (i.e., their magnitudes depend on the path followed during a process as well as the end states).
What are Path Functions? • Path functions have inexact differentials designated by the symbol , eg. Q and W. • Point functionshave exact differentials designated by the symbol , eg. V Properties are point functions, but heat and work are path functions.
Types of work • Mechanical Work • Moving boundary work (The most common form) • Shaft work • Spring work • Electric Work • An electric wire crossing the system boundaries, (We=V I t) • V =voltage • I=current • t =time
Two requirements for Mechanical work to exist • There must be a force on the boundary. • Example: the expansion of a gas into an evacuated space (is not work since there is no force). • The boundary must move. • Example: Fixed piston in the presence of external force (is not work since the boundary did not move).
Computing Moving Boundary Work • The area under the process curve on a P-V diagram represents the boundary work.
Net Work done in a cycle • The cycle shown in the figure (right) produces a net work output. • This is because the work done by the system during the expansion process (area under path A) is greater than the work done on the system during the compression part of the cycle (area under path B), • The difference between these two is the net work done during the cycle (the colored area). WA > 0 since V = V1 –V2 > 0 WB < 0 since V = V2 –V1 < 0 Wnet = WA +WB = Area bounded by the curve
Moving Boundary Work for quasi- equilibrium process • Strictly speaking the pressure in the integral is the pressure at the inner surface of the piston (Pi) • It becomes equal to the pressure in the cylinder only if the process is quasi- equilibrium. Thus the entire gas is at the same pressure at any given time
Moving Boundary Work for non-quasi- equilibrium process • For non-quasi-equilibrium process, we still can compute the work if the pressure at the inner surface of the piston is used for Pi. • We can not speak of pressure of a system during non-quasi-equilibrium process.
Computing the work for some special processes • Constant volume • Constant pressure • Isothermal • Polytropic
P V Constant Volume Process 1 2
P W V Constant Pressure Process 1 2
Example 3-6: Boundary Work during a Constant-Pressure Process A floating frictionless piston-cylinder device contains 10 lbm of water vapor at 60 psia and 320oF. Heat is now transferred to the steam until the temperature reaches 400oF. Determine the work done by the steam during this process. (Answer: 96.4 Btu)
P V Isothermal Process But for an ideal gas 1 2
Example 3-7: Boundary Work during an Isothermal Process A piston-cylinder device initially contains 0.4 m3 of air at 100 kPa and 80oC. The air is now compressed to 0.1 m3 in such a way that the temperature inside the cylinder remains constant. Determine the work done during this process. (Answer: -55.45 kJ)
Polytropic Process For General Gases, P and V are often related as
2 1 Lets go through that step-wise
Wb But… And…. So… Polytropic Process
So far, we have not assumed an ideal gas in this derivation, if we do, then…. Ideal gas undergoing a Polytropic Process
Computing the work of a Gas expanding against a Spring Spring just touching piston Spring exerting force on piston
2 2 Pressure W Volume Computing the Spring work alone 1 Spring exerting force on piston No Spring exerting force on piston V1 V2 V2
Example 3-9: Expansion of a Gas against a Spring A piston-cylinder device contains 0.05 m3 of gas initially at 200 kPa. At this state, a linear spring that has a spring constant of 150 kN/m is touching the piston but exerting no force on it. Now heat is transferred To the gas, causing the piston to rise and to compress the spring until the volume inside the cylinder doubles. If the cross-sectional area of the piston is 0.25 m2, determine (a) the final pressure inside the cylinder, (b) the total work done by the gas, and c) the fraction of this work done against the spring to compress it.
Example 3-8: Power transmission by the shaft of a car Determine the power transmission through the shaft of a car when the torque applied is 200 Nm and the shaft rotate at a rate of 4000rpm. (Answer: 83.8 kW)
How does energy cross an open system boundary? • The energy content of a control volume can be changed by mass flow as well as heat and work interactions
Mass Flow Rate • The amount of mass flowing through a cross section per unit time is called the mass flow rate. • It is given as • = density of fluid, Kg/m3 • Vm = mean velocity normal to A • A= cross sectional area of pipe. • Usually we drop the subscript m The unit is Kg/s
Volume Flow Rate • Volume flow rate is the volume of fluid flowing through a cross section per unit of time • It is given as • Vm = mean velocity normal to A • A= cross sectional area of pipe. • Usually we drop the subscript m The unit is m3/s
Conservation of mass principle _ Total mass entering the system Total mass leaving the system Net change in mass within the system = On a rate basis,
Conservation of mass principle (continued) For many inlets and exits, On a rate basis,
For steady process, no accumulation of mass in CV 0 For single stream,
Flow rate for Steady compressible flow ( = not const.) • Although, in a steady flow process, • Volume Flow Rates are not Necessarily the same • This is because
Special Case: Flow rate for Steady Incompressible Flow ( =constant) For single stream
Flow Work (Flow Energy) • Some people call it “flow energy” • Flow work is defined as the work required to push a unit mass of fluid into or out of a control volume. • It is equal to Pv
Flow Work derivation The force applied on the fluid by the imaginary piston is Wf per unit mass is
Total Energy of a Flowing Fluid Recall that The total energy of a system is For control volume, the fluid entering or leaving possesses an additional form of energy (the flow work or the flow energy) The total energy of a flowing fluid
Observations • Using h instead of u to represent the energy of a flowing fluid, results in • Taking care of the energy required to push the fluid in or out of the control volume. • In fact, this is the main reason behind introducing the enthalpy.
