Thermodynamics assignment help – 1.The industrial compression of ‘permanent’ gases is a mature technology perfected during the past one hundred years. The development was driven by the need to have low temperature refrigerants (cryogenics, liquefaction) and the separation of gaseous mixtures (e.g., air) into components needed for the chemical engineering industry.
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The gas compression technology was aided by simultaneous developments in turbomachinery, which were driven by the need to increase power generation in steam turbine power plants. This is why gas compression today is performed with adiabatic compressors followed by air-to-ambient heat exchangers (called aftercoolers in cryogenics). Several compressor-aftercooler pairs offer less irreversibility than a single compression stage. Furthermore, an adiabatic compressor that operates in the reversible limit (isentropically, ηc = 1) uses less power than a compressor that operates irreversibly (ηc < 1, where ηc is the compressor isentropic efficiency).
（1）Consider a single adiabatic and reversible compressor that brings the air stream ṁ from state 1 (PL, T1) to state “a” (PH, T > T1). The aftercooler places the stream (PH, T) in contact with ambient air and cools it down to T1. Derive the expression for the steady power requirement Ẇ1-a in terms of the pressure ratio π = PH/PL,
（2）Next, consider a reversible isothermal compressor that brings the ṁ stream from state 1 to state 2 by maintaining its temperature constant by thermal contact with the ambient all along the path 1-2. Derive the power required by a reversible isothermal compressor Ẇ1-2 as a function of π.
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（3）How much better is the isothermal compression relative to the adiabatic compression? Report the ratio Ẇ1-2 /Ẇ1-a as a function of π.
2. Consider next the expansion of the PH gas back to PL. If the reversible expander is adiabatic, the path of the stream is 2-b, which is followed by warming the gas back to T1 while mixing with the ambient.
(1) Derive the expression for the power delivered by the expander as a function of π. The ’round trip’ efficiency of compression-expansion operation in the reversible adiabatic limit is
ηround trip, adiabatic = Ẇ2-b /Ẇ1-a
and it depends on π. Calculate the adiabatic round-trip efficiency in the case of air and π = 10 and π = 100.
(2) Determine the round-trip efficiency of reversible isothermal compression and expansion. Compare the adiabatic and isothermal round-trip efficiencies, and comment on the potential rewards from isothermal compression and expansion. The difference indicates the opportunity even when the compressors and expanders operate irreversibly, because in such cases both round-trip efficiencies are lower than in the reversible limit.
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