Example Problems

Here are some example problems based on the material
in this lesson. I encourage you to read them,
think about them and maybe give them a try yourself. Then click on the
solution link at the end of each problem to see my solution and a good explanation.

Minimum Work for Compression of R-134a

4 pts

R-134a vapor enters an adiabatic compressor at -20oC and leaves at 700 kPa. If the R-134a is saturated when it enters the compressor, determine the minimum shaft work required by the compressor in kJ/kg.
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PVT Relationships for Isentropic, IG Processes

8 pts

Consider the Carnot Power Cycle shown in the PV Diagram, below. The working fluid is air and the specific heat ratio, γ, is constant.

Show that :
a.) V2/V1 = V3/V4
b.) (T2 / T3)γ = (P2 / P3)(γ-1)
c.) T2 / T3 = (V3 / V2)(ρg-1)
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Work & ΔS for IGs in Isothermal, Polytropic and Adiabatic Processes

8 pts

Argon gas is compressed in a piston and cylinder device from 20 psia and 55oF to 120 psia. The compression is internally reversible and the argon behaves as an ideal gas with a constant heat capacity of CP = (5/2) R.Determine the work in Btu/lbm and ΔS in Btu/lbm-oR and sketch the process path on both PV and TS Diagrams assuming the compression is :
a.) Polytropic with δ = 1.5
c.) Isothermal
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Performance of an Ideal Gas Cycle

10 pts

An ideal gas contained in a piston-and-cylinder device undergoes a thermodynamic cycle made up of three quasi-equilibrium processes.
Step 1-2: Adiabatic compression from 20oC and 110 kPa to 400 kPa
Step 2-3: Isobaric cooling
Step 3-1: Isothermal expansion
a.) Carefully draw this process in a traditional piston-and-cylinder schematic
b.) Sketch the process path for this cycle on a PV Diagram. Put a point on the diagram for each state and label it. Be sure to include and label all the important features for a complete PV Diagram for this system
c.) Calculate Q, W, ΔU and ΔH, in J/mole, for each step in the process and for the entire cycle. Assume that CP = (5/2) R.
d.) Is this cycle a power cycle or a refrigeration cycle? Explain. Calculate the thermal efficiency or COP of the cycle, whichever is appropriate.
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Power Input for an Internally Reversible, Polytropic Compressor

6 pts

Consider the internally reversible ammonia compressor shown below. The compression process is polytropic with δ = 1.27.

Determine Ws and Q in kW.
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