First Law Applied to a Closed system Most closed systems in practice are stationary, i.e. they do not involve kinetic energy and potential energy during the process. Thus the stationary systems are called nonflow systems. And the first law of thermodynamics is reduced to: In differential form: In the present of only p.dV work: In Integral form: Also for a cyclic process Δπ = 0, as the system regains its original state hence, π−π=0 ∴π=π Enthalpy At constant pressure: Specific heat cv According to I law of thermodynamics Specific heat cp Specific heat Perpetual Machine of I kind 1. below Fig Example 1 below 2. 2. 3. 4. First Law for an open system (1) (1) Steady Flow Energy Equation (SFEE) Assumptions The following assumptions are made in the steady flow system analysis: a) The mass flow through the system remains constant. b) Fluid is uniform in composition. c) The only interaction between the system and surroundings are work and heat. d) The state of fluid at any point remains constant with time. e) In the analysis only potential, kinetic and flow energies are considered. Steady Flow Energy Equation (SFEE) β’ Consider a flow of fluid through an open system as shown in earlier Figure. β’ During a small time interval ππ‘ there occurs a flow of mass and energy into the fixed control volume; entry is at section 1 and exit occurs at section 2. β’ The fluid enters the control volume at section 1 with average velocity πΆ1, Pressure π1, Specific volume π£1, and Specific internal energy π’1. β’ The corresponding values at the exit section 2 are πΆ2, π2, π£2 πππ π’2. β’ Further during, the fluid flow between the two selected sections, heat (π) and mechanical or shaft work (ππ ) may also cross the control surface. β’ The following species of energy are taken into account while drawing up the energy balance: A. Internal energy stored by the fluid = π B. Kinetic energy =(1/2)ππΆ2 C. Potential energy = πππ D. Flow work = π1π1 E. Heat interaction = π F. Work interaction i.e. shaft work = ππ According to 1st law of thermodynamics, energy balance in the symbolic form may be written as, Steady Flow Energy Equation (SFEE) But according to assumption (1): Also, enthalpy: β = π’ + ππ£ π = π1 = π2 SFEE on unit mass basis: Here, all the terms represents energy flow per unit mass of the fluid (J/kg) SFEE Applied to Engineering Applications βThe SFEE applies to flow processes in many of the engineering applications, such as Turbines, Compressors, Pumps, Heat exchangers and flows through nozzles and diffusers. βIn certain flow processes, some of the energy terms in SFEE are negligibly small and can be omitted without much error. 1. Nozzles and Diffusers A nozzle is a device for increasing the velocity of a steadily flowing steam at the expense of its pressure and hence enthalpy. A diffuser is a device that increases the pressure of a fluid by slowing it down. That is nozzles and diffusers perform opposite task. Nozzles and diffusers are commonly utilized in jet engines, rockets, spacecraft, and even garden hoses. Fig. below shows a commonly used convergent-divergent nozzle. 2. Heat Exchanger Boiler Condenser Evaporator β’ Condensers and Evaporators are the main types of heat exchangers. β’ These are the devices where the objective is to transfer heat energy between hot and cold fluids. Therefore, the heat transfer rate cannot be taken as zero. β’ These devices are widely used in refrigeration system, air conditioning system, thermal power plant and various industries. β’ A steam condenser is also a heat exchanger in which steam losses heat as it passes over the tubes through which cold fluid is flowing. β’ An evaporator is also a heat exchanger and is used to extract heat from the cold places or fluids. β’ Boiler is a type of evaporator and hence heat exchanger; used for the generation of steam. Thermal energy released by combustion of fuel is transferred to water which vaporizes and gets converted into steam at the desired pressure and temperature. Applying Steady Flow Energy Equation (SFEE), 3. Steam or Gas Turbine β’ A turbine is a device for obtaining work from a flow of fluid expanding from high pressure to low pressure. β’ The characteristic features of flow through a steam or gas turbine are: β’ Shaft work produced; ππ = +π£π β’ Negligible velocity change in the flow of fluid; πΆ1 = πΆ2 β’ Negligible potential energy change; π1 = π2 β’ No transfer of heat as its walls are thermally insulated; π = 0 Applying Steady Flow Energy Equation (SFEE), Hence, SFEE is reduced to, Apparently work is done at the expense of enthalpy. 4. Centrifugal Water Pump A centrifugal water pump is a device that transfers the mechanical energy of a motor or an engine into the pressure energy of incompressible fluid like water. Applying Steady Flow Energy Equation (SFEE), The characteristic features of flow through a centrifugal water pump are: Shaft work required; ππ = −π£π Negligible change in temperature of water so, Heat transfer rate from turbine; π = 0 Change in specific internal energy; Δπ’ = π’2 − π’1 = 0 As water is incompressible fluid, its specific volume and hence density will remain constant; π£1 = π£2 = π£ Hence, SFEE is reduced to, 5. Throttling Process Throttling is the expansion of fluid from high pressure to low pressure. This process occurs when fluid passes through an obstruction (partially opened valve, porous plug or a small orifice) placed in the fluid flow passage. The throttling process is commonly used for the following purposes : I. For determining the condition of steam (dryness fraction). II. For controlling the speed of the turbine. III. Used in refrigeration plant for reducing the pressure of the refrigerant before entry into the evaporator. Fig. below shows the schematic of porous plug experiment performed by Joule and Thomson in 1852. A stream of incompressible fluid is made to pass steadily through a porous plug placed in an insulated and horizontal pipe. Applying Steady Flow Energy Equation (SFEE), The characteristic features of a throttling process are: β No shaft work required; ππ = 0 β No heat interaction as pipe is thermally insulated; π = 0 β Negligible velocity change in the flow of fluid; πΆ1 = πΆ2 β Negligible potential energy changes as the pipe is placed horizontally; π1 = π2 Hence steady flow energy equation reduced to, β1 = β2 Enthalpy of fluid remains constant during throttling process. Thus the throttling expansion process is an isenthalpic process. For a perfect gas, πΆππ1 = πΆππ2 ∴ π1 = π2 Thus for a perfect gas, the temperature before and after throttling is always same. 2: Ex. 2, Fig. Ex. 2 Example 3: In water cooling tower air enters at a height of 1 m above the ground level and leaves at a height of 7 m. The inlet and outlet velocities are 20 m/s and 30 m/s respectively. Water enters at a height of 8 m and leaves at a height of 0.8 m. The velocity of water at entry and exit are 3 m/s and 1 m/s respectively. Water temperatures are 80°C and 50°C at the entry and exit respectively. Air temperatures are 30°C and 70°C at the entry and exit respectively. The cooling tower is well insulated and a fan of 2.25 kW drives the air through the cooler. Find the amount of air per second required for 1 kg/s of water flow. The values of cp of air and water are 1.005 and 4.187 kJ/kg K respectively. Example 4: Example 4) References βThermodynamics, An Engineering Approach by Yunus A. Cengel and Michael A Boles, McGraw-Hill Education. βEngineering Thermodynamics by P. K. Nag, Tata McGraw-Hill Education. βEngineering Thermodynamics Notes Prepared By: Bhavin J. Vegada, Department of Mechanical Engineering, Darshan Institute of Engineering & Technology, Rajkot.
