1st Law of Thermodynamics 4/8/2019

CO3: Ability to analyze using concepts and principles of First Law and Second Law of Thermodynamics. 4/8/2019

Objectives State and Explain the First Law of Thermodynamics Examine the boundary work (P dV work) Develop the general energy balance Calculate and solve energy balance problems for closed systems, steady- flow systems and some engineering devices 4/8/2019

THE FIRST LAW OF THERMODYNAMICS The first law of thermodynamics (the conservation of energy principle) provides a sound basis for studying the relationships among the various forms of energy and energy interactions. The first law states that energy can be neither created nor destroyed during a process; it can only change forms. Energy cannot be created or destroyed; it can only change forms. The increase in the energy of a potato in an oven is equal to the amount of heat transferred to it. In the absence of any work interactions, the energy change of a system is equal to the net heat transfer. 4/8/2019

The First Law: For all adiabatic processes between two specified states of a closed system, the net work done is the same regardless of the nature of the closed system and the details of the process. The work (electrical) done on an adiabatic system is equal to the increase in the energy of the system. The work (shaft) done on an adiabatic system is equal to the increase in the energy of the system. 4/8/2019

Energy Balance The net change (increase or decrease) in the total energy of the system during a process is equal to the difference between the total energy entering and the total energy leaving the system during that process.   The work (boundary) done on an adiabatic system is equal to the increase in the energy of the system. The energy change of a system during a process is equal to the net work and heat transfer between the system and its surroundings. 4/8/2019

Energy Change of a System, Esystem   OR Internal, kinetic, and potential energy changes 4/8/2019

Mechanisms of Energy Transfer, Ein and Eout Heat transfer to a system will increase the internal energy of the system while heat transfer from a system will decrease the energy of the system. Heat transfer, Q Work transfer to a system will increases the energy of the system while work transfer from a system will decrease the energy of the systems. Work transfer, W When mass enters a system, the energy of the system will increases because mass carries energy with it. Mass flow, m 4/8/2019

The heat transfer, Q is zero for adiabatic systems.   The heat transfer, Q is zero for adiabatic systems. The work transfer, W is zero for systems that involve no work interactions. The energy transport with mass, Emass is zero for systems that involve no mass flow across their boundaries (e.g. closed system) The energy content of a control volume (open system) can be changed by mass flow as well as heat and work interactions. 4/8/2019

Example 1: Cooling of a Hot Fluid in a Tank A rigid tank contains a hot fluid that is cooled while being stirred by a paddle wheel. Initially, the internal energy of the fluid is 800kJ. During the cooling process, the fluid losses 500kJ of heat and the paddle wheel does 100kJ of work on the fluid. Determine the final internal energy of the fluid. Neglect the energy stored in the paddle wheel. 4/8/2019

Solution: The tank is stationary and thus the kinetic and potential energy changes are zero, ∆KE=∆PE=0. Therefore, ∆E=∆U and internal energy is the only form of the system’s energy that may change during this process. Applying the energy balance on the system gives: Therefore, the final internal energy of the system is 400 kJ. 4/8/2019

Exercise 1: Water is being heated in a closed pan while being stirred by a paddle wheel. During the process, 30 kJ of heat is transferred to the water, and 5 kJ of heat is lost to the surrounding air. The paddle wheel work on the water is 500 J. Determine the final energy of the system if its initial energy is 10 kJ. Answers: E2 = 35.5 kJ 4/8/2019

BOUNDARY WORK, Wb Boundary work (P dV work): The expansion and compression work in a piston-cylinder device. Wb is positive  for expansion Wb is negative  for compression The work associated with a moving boundary is called boundary work. A gas does a differential amount of work Wb as it forces the piston to move by a differential amount ds. 4/8/2019

The boundary work done during a process depends on the path followed as well as the end states. The area under the process curve on a P-V diagram is equal, in magnitude, to the work done during a quasi-equilibrium expansion or compression process of a closed system. 4/8/2019

Boundary Work for a Constant Volume Process What is the boundary work for a constant-volume process? Example 2: A rigid tank contains air at 500 kPa and 150°C. As a result of heat transfer to the surroundings, the temperature and pressure inside the tank drop to 65°C and 400 kPa, respectively. Determine the boundary work done during this process.   4/8/2019

Boundary Work for a Constant Pressure Process Example 3: A frictionless piston cylinder device contains 5 kg of steam at 400 kPa and 200°C. Heat is now transferred to the steam until the temperature reaches 250°C. If the piston is not attached to a shaft and its mass is constant, determine the work done by the steam during this process.   4/8/2019

Exercise 2: The volume of 1 kg of refrigerant-134a in a piston cylinder device is initially 0.13741 m3. Now, refrigerant is compressed until half of its original volume while the pressure is maintained constant at 180 kPa. Determine the initial and final temperatures of refrigerant as well as the work required to compress it, in kJ. Answers: T1 = 40°C T2 = -12.73°C Wb = -12.357 kJ 4/8/2019

Boundary Work for an Isothermal Process Example 4: 1 m3 of saturated liquid water at 200°C with the mass of 100 kg is expanded isothermally in a closed system until its quality is 80 percent. Determine the total work produced by this expansion, in kJ.           4/8/2019

Exercise 3: A tank initially contains 0.4 kg of water at 100 kPa and 150°C. The water is now expanded isothermally to a pressure of 50 kPa. Determine the boundary work during this process. Answers: Wb = 146.475 kJ 4/8/2019

ENERGY BALANCE FOR CLOSED SYSTEMS Energy balance for any system undergoing any process     Energy balance in the rate form The total quantities are related to the quantities per unit time is     Energy balance per unit mass basis 4/8/2019

Energy balance relations with sign conventions Energy balance for a cycle +ve sign  heat transfer to (Qin) work done by (Wout) -ve sign  heat transfer from (Qout) work done on (Win) For a cycle E = E2 – E1 = 0 or Ein – Eout = 0 thus Ein = Eout       Various forms of the first-law relation for closed systems when sign convention is used.   4/8/2019

Example 5: A 0.5 m3 rigid tank contains refrigerant-134a initially at 160 kPa and 40 percent quality. Heat is now transferred to the refrigerant until the pressure reaches 700 kPa. Determine: The mass of the refrigerant in the tank The amount of heat transferred 4/8/2019

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Exercise 4: A 0.6 m3 rigid tank initially contains saturated R-134a vapor at 1200 kPa. As a result of heat transfer from the refrigerant, the pressure drops to 400 kPa. Determine: The final temperature The amount of heat transferred Answers: T2 = 8.91°C Qout = 4883 kJ 4/8/2019

ENERGY ANALYSIS OF STEADY-FLOW SYSTEMS Under steady-flow conditions, the mass and energy contents of a control volume remain constant. Many engineering systems such as power plants operate under steady conditions. Under steady-flow conditions, the fluid properties at an inlet or exit remain constant (do not change with time). 4/8/2019

Mass balances for steady-flow processes A water heater in steady operation. Where; ρ is density, V is the average flow velocity in the flow direction, A is the cross-sectional area normal to the flow direction. 4/8/2019

Total Energy of Non-flowing and Flowing Fluid The flow energy is automatically taken care of by enthalpy. In fact, this is the main reason for defining the property enthalpy. h = u + Pv 4/8/2019 The total energy consists of three parts for a nonflowing fluid and four parts for a flowing fluid.

Energy Transport by Mass of Flowing Fluid When the kinetic and potential energies of a fluid stream are negligible 4/8/2019

Energy balances for a steady-flow process 4/8/2019

Energy balance relations with sign conventions (heat input and work output are positive) when kinetic and potential energy changes are negligible Some energy unit equivalents 4/8/2019

SOME STEADY-FLOW ENGINEERING DEVICES Many engineering devices operate essentially under the same conditions for long periods of time. The components of a steam power plant (turbines, compressors, heat exchangers, and pumps), for example, operate nonstop for months before the system is shut down for maintenance. Therefore, these devices can be conveniently analyzed as steady-flow devices. A modern land-based gas turbine used for electric power production. This is a General Electric LM5000 turbine. It has a length of 6.2 m, it weighs 12.5 tons, and produces 55.2 MW at 3600 rpm with steam injection. 4/8/2019

Nozzles and Diffusers Nozzles and diffusers are commonly utilized in jet engines, rockets, spacecraft, and even garden hoses. A nozzle is a device that increases the velocity of a fluid at the expense of pressure. A diffuser is a device that increases the pressure of a fluid by slowing it down. The cross-sectional area of a nozzle decreases in the flow direction for subsonic flows and increases for supersonic flows. The reverse is true for diffusers. Energy balance for a nozzle or diffuser: Nozzles and diffusers are shaped so that they cause large changes in fluid velocities and thus kinetic energies. 4/8/2019

Deceleration of Air in a Diffuser 4/8/2019

Acceleration of Steam in a Nozzle 4/8/2019

Example 6: Steam at 1.8 MPa and 400°C steadily enters a nozzle whose inlet area is 0.02 m2. The mass flow rate of steam through the nozzle is 5 kg/s. Steam leaves the nozzle at 1.4 MPa with a velocity of 275 m/s. Heat losses from the nozzle per unit mass of the steam are estimated to be 2.8 kJ/kg. Determine: The inlet velocity The exit temperature of the steam Solution:   (Table A-6) 4/8/2019

Solution: P2 = 1.4 Mpa h2 = 3211.9 kJ/kg From table A-6, T2 = 378.6°C   P2 = 1.4 Mpa h2 = 3211.9 kJ/kg From table A-6, T2 = 378.6°C 4/8/2019

Exercise 5: Steam at 3 Mpa and 400°C enters an adiabatic nozzle steadily with a velocity of 40 m/s and leaves at 2.5 Mpa and 300 m/s. Determine the exit temperature. Answers: T2 = 376.7°C 4/8/2019

Turbines and Compressors Turbine drives the electric generator in steam, gas, or hydroelectric power plants. As the fluid passes through the turbine, work is done against the blades, which are attached to the shaft. As a result, the shaft rotates, and the turbine produces work. Compressors, as well as pumps and fans, are devices used to increase the pressure of a fluid. Work is supplied to these devices from an external source through a rotating shaft. A fan increases the pressure of a gas slightly and is mainly used to mobilize a gas. A compressor is capable of compressing the gas to very high pressures. Pumps work very much like compressors except that they handle liquids instead of gases. Energy balance for the compressor in this figure: 4/8/2019

Compressing Air by a Compressor 4/8/2019

Power Generation by a Steam Turbine 4/8/2019

Example 7: The power output of an adiabatic steam turbine is 5 MW, and the inlet and the exit conditions of the steam are as indicated in figure. Determine: The magnitude of Δh, Δke, and Δpe The work done per unit mass of the steam flowing through the turbine 4/8/2019

Solution:   (Table A-6) 4/8/2019

Solution:   4/8/2019

Exercise 6: Refrigerant-134a enters a compressor at 180 kPa as a saturated vapor with a volume flow rate of 0.35 m3/min and leaves at 700 kPa. The power supplied to the refrigerant during compression process is 2.35 kW. What is the temperature of R-134a at the exit of the compressor? Answers: T2 = 48.8°C 4/8/2019

Throttling valves Energy balance Throttling valves are any kind of flow-restricting devices that cause a significant pressure drop in the fluid. What is the difference between a turbine and a throttling valve? The pressure drop in the fluid is often accompanied by a large drop in temperature, and for that reason throttling devices are commonly used in refrigeration and air-conditioning applications. Energy balance The temperature of an ideal gas does not change during a throttling (h = constant) process since h = h(T). During a throttling process, the enthalpy of a fluid remains constant. But internal and flow energies may be converted to each other. 4/8/2019

Mixing chambers 10C 60C 43C 140 kPa In engineering applications, the section where the mixing process takes place is commonly referred to as a mixing chamber. Energy balance for the adiabatic mixing chamber in the figure is: The T-elbow of an ordinary shower serves as the mixing chamber for the hot- and the cold-water streams. 4/8/2019

Mixing of Hot and Cold Waters in a Shower 4/8/2019

Heat exchangers Heat exchangers are devices where two moving fluid streams exchange heat without mixing. Heat exchangers are widely used in various industries, and they come in various designs. The heat transfer associated with a heat exchanger may be zero or nonzero depending on how the control volume is selected. Mass and energy balances for the adiabatic heat exchanger in the figure is: A heat exchanger can be as simple as two concentric pipes. 4/8/2019

Pipe and duct flow The transport of liquids or gases in pipes and ducts is of great importance in many engineering applications. Flow through a pipe or a duct usually satisfies the steady-flow conditions. Pipe or duct flow may involve more than one form of work at the same time. Energy balance for the pipe flow shown in the figure is Heat losses from a hot fluid flowing through an uninsulated pipe or duct to the cooler environment may be very significant. 4/8/2019