 # isentropic process example problems

A simple example of isentropic but non-adiabatic and irreversible process: a working isothermal damper (loose piston in a cylinder with a viscous liquid) which is in … 0000002147 00000 n With this we can calculate the actual entropy, $latex s_{actual} = 0.3356 + 0.505(1.3962) = 1.0407 \frac {btu}{lbm R}&s=2$, Next we take the actual and ideal entropies and find the isentropic efficiency, $latex \eta = \frac {1.0407 \frac {btu}{lbm R}}{1.4634 \frac {btu}{lbm R}} = 0.7111&s=2$, Choice C is the correct answer An aircraft gas turbine with an isentropic efficiency of 85% receives hot gas from the combustion chamber at 10 bar and 1000 °C. Since helium behaves almost as an ideal gas, use the ideal gas law to calculate outlet temperature of the gas ( T4,is ). Total Density: 09/12/2010 Dr. Munzer Ebaid 3 5. 0000002382 00000 n • When n=1, pV = constant, and the process is a constant temperature or an isothermal process. 0000001887 00000 n WORKED EXAMPLE No.2 A gas turbine expands gas from 1 MPa pressure and 600oC to 100 kPa pressure. Solution: Two isentropic processes and two isobaric processes. Calculate the exit temperature and the power output. 0000008319 00000 n Problem (12.16) IsentropicFlow d cm V m s t Given T C P t kPa 2 250 20 500 = = = =,: o , 2 2 1 The volume of the inert gas is 0.05 cubic meters at the temperature of 140 degree centigrade and 125 KPa pressure. Assume an isentropic expansion of helium ( 3 → 4) in a gas turbine. 0000000795 00000 n So generally an adiabatic process is not necessarily isentropic -- only if the process is reversible and adiabatic we can call it isentropic. 131 0 obj<> endobj Our goal is to help people practice for the FE and PE exams, Posted June 6, 2014 by Patrick Matherne in category ". Problem Answer: a.) "! Some examples of theoretically isentropic thermodynamic devices are pumps, gas compressors, turbines, nozzles, and diffusers. Q=0 s=0, where k is the ratio of specific heats Example (FEIM): In an isentropic compression of an ideal gas, p1 = 100 kPa, p2 = 200 kPa, V1 = 10 m3, and k = 1.4. Isentropic Process (Adiabatic reversible) 3. 0000005516 00000 n 131 24 Example: Isentropic Expansion in Gas Turbine Ideal Brayton cycle consist of four thermodynamic processes. Calculate T 2 and the entropy generation if a real piston-and-cylinder device requires 15% more work than the internally reversible device. $latex Quality\ =\ \frac {s_f – s_{actual}}{s_{fg}}&s=2$, $latex \eta = \frac {s_{actual}}{s_{ideal}}&s=2$. Modeling this carbon dioxide leak process as an isentropic process. Modern gas turbine engines and airbreathing jet engines also follow the Brayton cycle. An adiabatic process is a process with no heat transfer (). Find V 2.! %%EOF Gas compression occurs in isentropic process. Some specific values of n correspond to particular cases: = for an isobaric process, = + ∞ for an isochoric process. The outlet temperature from a real, adiabatic compressor that accomplishes the same compression is 520K.Calculate the actual power input and the isentropic efficiency of the real compressor. xref 0000052330 00000 n 0000001520 00000 n First we need to find the entropy for the ideal conditions. 3. 0000003370 00000 n In order to find the efficiency you will need to calculate the actual entropy. Take cv = 718 J/kg K and cp = 1005 J/kg K SOLUTION The process is adiabatic so the ideal temperature T2' is given by T2'=T1(rp) 1-1/γ An Irreversible process can't be in a quasi-static state (the process that happens slowly to keep it in an equilibrium) A reversible process is a quasi-static process. 0000001737 00000 n 0000004855 00000 n 0000052152 00000 n s 1 = s 2. Hence the stagnation temperature can be written T0 = constant and P0 = constant and both of them are … If the compression ratio V1/V2 of this engine is 8, determine the final temperature of the air using: a) Variable specific heats, … In the calculations adiabatic k-value for air is assumed to be 1.4, and gas constant for air R - 286 J/(kg*К). Isentropic Process In an adiabatic process: Q = 0 An isentropic process is a special case of an adiabatic process where the process is entirely reversible. In order to solve this problem you will need to use steam charts (ASME Steam Tables are recommended, but you can probably find some free ones on the web).First we need to find the entropy for the ideal conditions. (a) Note that h = W cycle /Q in = (W 12 + W 34)/Q 12 because Q 23 and Q 41 are equal and have opposite signs. 0000052555 00000 n DEFINITION: Isentropic Process is a reversible adiabatic process. Example: Isentropic Expansion in Gas Turbine. A worker brought in a bottle, which needs to be refilled because of the leak from the broken spray probe. {\displaystyle s_ {1}=s_ {2}} . Kinetic Pressure: 6. Calculate the minimum power input required and T 2: b.) a.) An example of such a process is the expansion valve in a refrigerant cycle. The reason is that if the process is irreversible you will not come back to the same state: if the volume is the same, pressure and temperature will differ, as the work made by the piston when coming back and forth will not net zero, and the internal energy will change. ΔS wiggle is zero for an isentropic process and this lets us simplify the Gibbs Equations Now, let’s apply both of the ideal gas Gibbs Equations to an isentropic process that begins at the reference state that we chose for the ideal gas entropy function and proceeds to … TOPIC: Processes of Ideal Gas. Copyright © 2014. Regarding you example of an irreversible adiabatic cycle: It is impossible and the example is flawed. One chamber contains air at 500 K and 2 MPa. Examples of how to use “isentropic” in a sentence from the Cambridge Dictionary Labs An isentropic process is an idealization of an actual process, and serves as a limiting case for an actual process. Chapter 6 Black Board Answer Sheet 6 Problem sheet 3- ans Problem sheet 5 ans(1) Other related documents Managerial Coursework (predatory pricing) Banks Exam January 2014, questions Exam January 2014, answers Exam final January 2015, answers Problem sheet 2 An adiabatic process is defined as a process in which no heat transfer takes place. Wn = -44.35 kJ/s b.) 0000005338 00000 n Let assume the ideal Brayton cycle that describes the workings of a constant pressure heat engine. The isentropic efficiency 0.92. Where is the ratio of the heat capacity at constant pressure to heat capacity at constant volume ().. Equivalence between the polytropic … • When n=k, it is an called isentropic process. ft to a final volume of 3.6 cu. P-V diagram of an isentropic expansion of helium (3 → 4) in a gas turbine. Compare h obtained this way with the … B) 81% Example 4.5.1: a turbine. In order to solve this problem you will need to use steam charts (ASME Steam Tables are recommended, but you can probably find some free ones on the web). 0000044342 00000 n Example: A freezing process 5. Total Temperature: 5. Concept of isentropic process and one problem-solving demonstration, using thermodynamic property table. p V p Vn constant 2 2 n 1 1 = = : Notice that in part (a) the problem … You are evaluating a turbine that has dry steam entering at 500 psia and the steam is then is expanded isentropically and leaves the turbine at 20 psia. If cp = 0.124 and cv = 0.093 BTU/lb.°R, what are (a) T2 (b) P2 (c) ∆H and (d) W. Course: Thermodynamics. It expands this to the atmospheric pressure of 1 bar. A) 96% We defined for reversible processes . Process : Constant volume since the gas is stirred in an rigid container 3 .922 kJ/K = Comment : Though this process is adiabatic it is not isentropic since the process of stirring is an irreversible process. This does not mean that the temperature is constant, but rather that no heat is transferred into or out from the system. Assume an isentropic expansion of helium (3 → 4) in a gas turbine. Examples of how to use “adiabatic process” in a sentence from the Cambridge Dictionary Labs This will be illustrated by two examples: a turbine that produces a work output; and a compressor that absorbs a work input. Reference: In a prefect crystal of a pure substance at T =0K, the molecules are com- Assume an isentropic expansion of helium ( 3 → 4) in a gas turbine. 0000005010 00000 n %PDF-1.5 %���� trailer V2 = 0.113 m^3/s c.) ∆U = 45.05 kJ/s d.) ∆H = 59.33 kJ/s Problem: It is necessary to calculate isentropic efficiency of the compressor η is. : b.) 0000059460 00000 n a.) 0000000016 00000 n 1 Example 5 1.1 Solution 2 Example 6 2.1 Solution 3 Example 7 3.1 Assuming 3.2 Solution 4 Example 8 4.1 Assuming 4.2 Solution 5 Example 9 5.1 Solution 6 Example 10 6.1 Solution 7 Example 11 7.1 Solution Air is contained in a piston-cylinder arrangement (see sketch). Example of Isentropic Process Example: Isentropic Expansion in Gas Turbine P-V diagram of an isentropic expansion of helium (3 → 4) in a gas turbine. ̍Vڈw6�].�o��)A�r"�H>�7��U�%n���DmR"��S�q�0Q�m|Q"�)i���elꇰ�s�Qos��ؿRM����Y�MT��_����_~BC̝�<��ng�.E�qO�����c9_�A���)�6s��)M`N� \IT���f}��ʙ� E�e��ZQ�0j�0�qV��y���F���v��B#݁����h h2�e��s:�Zm��?���Aj�0�������oz�;���l�|��ѻaa�. Isentropic efficiencies of steady-flow devices in thermodynamic systems. I hope you remember that any process that is both internally reversible AND adiabatic is isentropic. 0000002346 00000 n : Read : Assume ideal gas behavoir for air.Apply an energy balance and an entropy balance. D) 63%. ft. C) 71% In compressor theory, the terms adiabatic (no heat transfer) and isentropic (constant entropy) are used interchangeably. P-V diagram of an isentropic expansion of helium (3 → 4) in a gas turbine. Tags: Isentropic Efficiency startxref Prob : 5.6 An insulated rigid vessel is divided into two chambers of equal volumes. Problem statement: Some amount of inert gas is entrapped in a piston cylinder. In addition, when the ideal gas law applies: = for an isothermal process, = for an isentropic process. Adiabatic Process. 0000005649 00000 n A reversible adiabatic is one of constant entropy. 0000001952 00000 n Remarks • When n=0, p = constant, and the process is a constant pressure or an isobaric process. Determine W 12 in terms of V 1, V 2, and T H (temperature of high temp reservoir) and also W 34 in terms of V 3, V 4, and T C.Note the relationship between Q 12 and W 12 determined from an energy balance during step 1-2. Example: Isentropic Expansion in Gas Turbine. Isentropic Process Ideal Gas Example 11 Air is compressed in a car engine from 22°C and 95 kPa in a reversible and adiabatic manner. {\displaystyle \Delta s=0} or. The mass flow rate is 12 kg/s. All rights reserved. When the pressure is 500 psia, the water is all steam so the entropy (s) is 1.4634 btu/lbm R. Particular cases. Δ s = 0. Adiabatic simply means no heat. Problem Description Click to View Movie (112 kB) Jim is in charge of filling the compressed carbon dioxide bottles in his factory. • When nÆ∞, it is called an isometric process. View the previous Question of the Day. The … Calculate the final temperature, T 2, and the boundary work if the process is internally reversible. 134 0 obj<>stream Solution. : Read : Determine S o (T 2) for an isentropic process and then interpolate to obtain both T 2S and H 2S.Then, an energy … If the leaving steam is found to have a quality of 50.5%, what is the isentropic efficiency of the turbine? Now, as you know all the necessary equations, let’s try to apply the equations for solving a typical problem. Problem Statement: Two pound of an ideal gas undergoes an isentropic process from 93.5 psig and a volume of 0.6 cu. Heat is added very slowly, and the piston is allowed to move out for each increment of heat added. 0000001384 00000 n Today’s PE/EIT exam question is about the isentropic efficiency of a turbine. For example a real compressor can be assumed adiabatic but is operating with losses. Isenthalpic means “Constant Enthalpy”, or constant total heat. The pressure decreases from the condenser to the evaporator but the enthalpy remains the same. Solution 11.3 The stagnation conditions at the reservoir will be maintained throughout the tube because the process is isentropic. When the pressure is 500 psia,  the water is all steam so the entropy (s) is 1.4634 btu/lbm R. At 20 psia the entropy is 0.3356 btu/lbm R for a saturated liquid and 1.3962 btu/lbm R for the mixed region. 0000001604 00000 n Theme "Anarcho Notepad" designed and engineered by Arthur "Berserkr" Gareginyan. Since helium behaves almost as an ideal gas, use the ideal gas law to calculate outlet temperature of the gas ( T4,is ). Some examples of theoretically isentropic thermodynamic devices are pumps, gas compressors, turbines, nozzles, and diffusers . A process during which the entropy remains constant is called an isentropic process, written. <<52bc77ff8723b44b8ef125d1bf632032>]>> Most steady-flow devices operate under adiabatic conditions, and the ideal process for these devices is the isentropic process. 0000002782 00000 n 0 Static Pressure Ratio across A Normal Shock Waves: 8. SUBTOPIC: Isentropic Process Gas for this problem is assumed to be incompressible (compressibility factor z=1). Application-based questions Q1: Let's take an example of the daily based activity, of pumping air …