1.A cylinder/piston contains 2 kg of methane gas at 900 kPa and 25ºC. If the gas expands reversibly to a pressure of 100 kPa, calculate the work produced (in kJ) for each of the following cases:I.Adiabatic (for example, rapid expansion)II.Isothermal (for example, very slow expansion)III.Polytropic, with n = 1.2 (this case is in-between I and II)IV.IsentropicV.Steam enters an ADIABATIC turbine at 200 psia, 900°F and exits at 40 psia, 600°F.
a.What is the actual work produced by the turbine (in BTU/lbm)
b.What is the ideal adiabatic work (in BTU/lbm) for the steam exiting at 40 psia (in this case the exittemperature is unknown).
c.What is the isentropic efficiency?
d.What is the generated entropy, Ŝgen (in BTU/R-lbm)?
3.Consider a top secret military power supply for arctic environment operations that will produceelectrical power from the soldier’s body heat. Model this power supply as a Carnot-cycle heat ENGINEthat uses R-22 as its working fluid. The boiler operates at 30ºC and converts saturated liquid into saturatedvapor. The condenser operates at -5ºC.
a.Show the cycle on a T-Ŝ (temperature vs. specific entropy) diagram relative to the 2-phase region andindicate, with arrows, the directions of working fluid flow.
b.Determine the required operating pressures of the boiler and condenser (in kPa).
c.Determine the quality of the R-22 at the entrance and exit of the condenser.
4.Reconsider the top-secret military power supply for artic environments that you worked in a previoushomework. Previously, you modeled it as a Carnot cycle; now you will use the more realistic Rankine cycle.The boiler operates at 1000 kPa with a maximum temperature of 30°C. The condenser is isobaric andoperates at -5°C.
a.Calculate the vapor quality leaving the turbine and the specific enthalpy exiting the turbine (in kJ/kg)
b.Determine the specific-work produced by the Rankine cycle turbine (in kJ/kg), assuming it is ideal(reversible) and adiabatic.
c.Show the cycle on a T-Ŝ (temperature vs. specific entropy) diagram relative to the 2-phase region andlabel the isobaric pathway of the boiler with its pressure (in kPa).
d.Determine the specific-work required by the Rankine cycle pump (in kJ/kg), assuming it is ideal(reversible) and adiabatic.
e.Determine the specific-QH for the Rankine cycle (in kJ/kg).
f.Calculation the Rankine cycle (thermal) efficiency
g.Compare the required material strength (using maximum cycle pressure) and cycle efficiency of thisRankine cycle with a Carnot cycle operating with the same TH (30°C) and TL (-5°C) by calculating thepercent change in max pressure and thermal efficiencies.
5. Air with T = 300 K and P = 100 kPa enters a Brayton-cycle compressor inlet. The combustion chamber adds 670 kJ/kg of air. Due to material considerations, the maximum gas temperature allowed is 1200 K. Assume ideal gas, a polytropic process, and the values in Table A.5 are valid.
The polytropic equations summarized on page 295 (Chapter 6) are valid for open and closed systems for P, T, and V only. HOWEVER, the polytropic specific work equations are only valid for closed systems. You cannot use them to calculate compressor and turbine work.
a. What is the maximum allowable compression ratio?
b. For the maximum allowable compression ratio, what is the net work?
c. What percentage of the turbine work is needed to drive the compressor?
d. For the maximum allowable compression ratio, what is the cycle efficiency?
e. SKETCH a TS diagram for this process, showing the cycle relative to the 2-phase region
6. A four-stroke gasoline engine has a compression ratio of 10:1 with 4 cylinders of total displacement of 2.3 L. The inlet conditions are 280 K and 70 kPa. The engine runs at 2100 RPM, with the fuel adding 1800 kJ/kg during combustion. Assume the fuel air mix has the properties of air.
a. What is the net work of the cycle
b. What is the power produced by the engine
c. A turbo charger with intercooler increases the inlet pressure, does this increase the power, thermal efficiency or both?
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