ES31 Energy Transfer Fundamentals Unit B: The First Law of Thermodynamics ROAD MAP... B-1: The Concept of Energy B-: Work Interactions B-3: First Law of Thermodynamics B-4: Heat Transfer Fundamentals Unit B-1: List of Subjects Conservation of Energy Energy of a System Energy Interactions and Transfer Thermodynamic Processes
PAGE 1 of 8 Conservation of Energy A refrigerator operating with its door open in a well-sealed and well-insulated room A fan running in a well-sealed and well-insulated room will raise the temperature of air in the room CONSERVATION OF ENERGY PRINCIPLE Conservation of Energy means (as an exact sense) the conservation of ONLY the quantity of energy (the statement of the first law of thermodynamics) The average room temperature... will it increase, decrease, or remain constant? A refrigerator operating its door open in a well-sealed and well-insulated room A fan running in a well-sealed and well-insulated room Electricity (the higher quality of energy) can always be converted to an equal amount of thermal energy (or often called just heat ) However, only a small fraction of thermal energy (the lower quality of energy) can be converted back to electricity ENERGY OF A SYSTEM: THREE TYPES OF ENERGY Internal Energy (U) Potential Energy (PE) PE mgz where, m = mass of the system, g = gravitational acceleration, and z = height or elevation V Kinetic Energy (KE) KE m where, m = mass of the system and V = velocity
PAGE of 8 Energy of a System (1) Internal energy Potential Energy Kinetic energy ENERGY PER UNIT MASS It is often convenient to define energy per unit mass (amount of energy for a given unit mass of the system): Internal Energy per unit mass (u) PE Potential Energy per unit mass (pe) pe gz m KE V Kinetic Energy per unit mass (ke) ke m TOTAL ENERGY OF A SYSTEM The total energy of a system (E) or the total energy per unit mass of a system (e = E / m) is the total sum of three types of energy: Total energy of a system is: E = U + KE + PE = V U m mgz Total energy of a system (per unit mass) is: e = u + ke + pe = V u gz ENERGY OF A CLOSED SYSTEM Most closed systems (control mass or CM ) remain stationary during a process and thus experience no change in their kinetic and potential energies. Closed systems whose velocity and elevation of the center of gravity remain constant during a process are frequently referred to as stationary systems.
PAGE 3 of 8 Energy of a System () Mass and energy flow rates associated with the flow of stream in a pipe Energy Rate (Power) ENERGY OF AN OPEN SYSTEM Control Volumes (CVs) typically involve fluid flow with a velocity ( convection ), and it is convenient to express the energy flow associated with a fluid stream in the rate form. The mass flow rate is defined as: m V AV c avg (kg/s) where, = mass of the system, Ac = cross-sectional area of flow, and Vavg = average flow velocity normal to Ac The energy flow rate (called, power ) is defined as: E me (kj/s or kw) MECHANICAL ENERGY OF A SYSTEM Mechanical energy is the form of energy that can be converted to mechanical work. If an ideal mechanical device exists, this is the amount of energy that can be completely converted to work. p V Mechanical energy per unit mass is defined as: emech gz Flow Work (per unit mass) Kinetic Energy (per unit mass) Potential Energy (per unit mass) Mechanical energy rate (or power ) is defined as: p V Emech memech m gz p p1 V V1 e g z z Change in mechanical energy for incompressible fluid: p p V V mech 1 1 1 In energy rate (power) form: E me m g z z mech mech 1
PAGE 4 of 8 EXERCISE B-1-1 (Do-It-Yourself) A site evaluated for a potential wind farm is observed to have steady winds at a speed of 8.5 m/s (shown in the figure). Determine the available wind energy (a) per unit mass (in J/kg ), (b) for a mass of 10 kg of air (in J ), and (c) for a flow rate of 1,154 kg/s for air (in kw ). Potential site for a wind farm Solution A site with a specified wind speed is considered. Wind energy per unit mass, for a specified mass, and for a given mass flow rate of air are to be determined. Assumptions Wind flows steadily at the specified speed. The only form of energy that can be harvested from air is the kinetic energy, which can be captured by a wind turbine. Analysis (a) Wind energy per unit mass of air is: V 8.5 m/s e ke 36.1 J/kg (b) Wind energy for an air mass of 10 kg is: E me 10 kg36.1 J/kg 361 J (c) Wind energy for a mass flow rate of 1,154 kg/s is: E me 1,154 kg/s36.1 J/kg 41,700 W (41.7 kw) Discussion The specified mass flow rate corresponds to a 1-m diameter flow section, if the air density is 1. kg/m 3. This analysis concludes that a wind turbine with a turbine diameter of 1 m has a power generation potential of 41.7 kw
PAGE 5 of 8 At a certain location, strong wind is blowing steadily at 10 m/s. Determine the mechanical energy of air per unit mass (in J/kg ) and the power generation potential of a wind turbine with 60-m-diameter blades at that location (in kw ). Take the air density to be 1.5 kg/m 3. Assumption The wind is blowing steadily at a constant uniform velocity Properties 3 The density of air is given: 1.5 kg/m Analysis Kinetic energy of the wind is the only form of mechanical energy that can be converted to work. Therefore, the power potential of the wind is essentially the kinetic energy of the wind: V 10 m/s emech ke 50 J/kg Mass flow rate can be defined as: 3 m VA V D 1.5 kg/m 10 m/s 60 m 35,340 kg/s 4 4 The power generation potential is, therefore: Emech memech 35,340 kg/s50 J/kg 1,770,000 W (1,770 kw) Discussion The power generation of a wind turbine is proportional to the cube of the wind velocity, and thus the power generation potential will depend strongly on the wind conditions.
PAGE 6 of 8 Energy Interactions and Transfer Energy can cross the boundaries of a closed system in the form of heat and work Directions of heat and work transfer WORK, ENERGY, AND POWER The unit of work is defined as: force applied distance moved The unit of work and energy are identical (exact same unit) The work can be understood as an amount of energy transferred through interaction The unit of power is defined as: energy time The power can be understood as a time rate of change of energy or energy transferred through interaction ENERGY INTERACTIONS Energy is transferred by IN or OUT interactions to or from Control Mass (CM) or Control Volume (CV) across the system boundary Heat interaction: is defined as energy transfer by temperature difference (temperature flow) Heat Energy IN = Qin and Heat Energy OUT = Qout Work interaction is defined as energy transfer by work (work input/output) Work Energy IN = Win and Work Energy OUT = Wout Heat and work interactions per unit mass can be defined as: W w and m Q q (kj/kg) m
PAGE 7 of 8 Thermodynamic Processes During an adiabatic process, a system exchanges no heat with its surroundings Properties are point functions; but heat and work are path functions (their magnitudes depend on the path followed) THERMODYNAMIC PROCESSES In thermodynamic analysis, one must clearly understand the importance of process Properties are point functions d V V ( Change of volume is independent to the process path: V VV 1) 1 Heat and work interactions are path functions (depends on the path followed during the process) W W1 W ( Work interaction depends on the process path: W1 W W1 1 ) THERMODYNAMIC MODELS FOR SIMPLIFIED ANALYSIS Isolated system: assumed no interactions of any kind across the system boundary Adiabatic process: no heat interaction (no energy transfer due to temperature difference) Isothermal process: constant temperature throughout the process
PAGE 8 of 8 EXERCISE B-1- (Do-It-Yourself) A candle is burning in a well-insulated room (isolated system). Taking the room (the air plus the candle) as the system, determine (a) if there is any heat transfer (across the boundary) during this burning process and (b) if there is any change in the internal energy of the system. Solution A candle burning in a well-insulated room is considered. It is to be determined whether there is any heat transfer and any change in internal energy. Analysis (a) The interior surfaces of the room from the system boundary is indicated by the dashed lines in the figure. Heat is recognized as it crosses the boundaries. Since the room is well insulated, we have an adiabatic system and no heat will pass through the boundaries. Q 0 (b) The internal energy involves energies that exist in various forms (sensible, latent, chemical, nuclear). During the process, part of the chemical energy is converted to sensible energy. However, there is no increase or decrease in the total internal energy of the system. U 0 Discussions Sensible Energy: the portion of the internal energy associated with the kinetic energies of the molecules (translation, rotation, and vibration of molecules) Latent Energy: the portion of the internal energy associated with the phase of the system (phase-change will cause the change in internal energy: the gas phase is at a higher internal energy level than liquid or solid phases) Chemical Energy: the portion of the internal energy associated with atomic bonds in a molecule (chemical reaction causes the destruction of atomic bonds and will change the internal energy) Nuclear Energy: the tremendous amount of energy associated with the strong bonds within the nucleus (can be released only through fusion or fission)