WS T5 (rev. 3.0)Page 29A heat engine uses an ideal gas of Nmonatomic particles as its working substance.The engine runs on the following four-stepcycle.iStmica2poTransformation 1+2 is isobaricTransformation 2-3 is adiabaticTransformation 3→4 is isobaricTransformation 4 1 is isochoricPo34VVo3V.Questionsa) Find the efficiency of this engine. You may find it helpful to organize your work as follows:Step1- 22→ 3AEnetWQ3 -441WnetQinb) Where in this cycle does the gas reach itshighest and lowest temperatures? Find theseextreme temperatures. (Your answers shouldabapossible? *be in terms of po, Vo, and N.)d) Are your answers consistent with the fact thatthe Carnot engine is the most efficient enginec) What would be the efficiency of a Carnotengine operating between these twotemperatures?•...

Hello. Since your question has multiple parts, we will solve the first part for you. If you want any other parts to be solved, then please resubmit the whole question and specify those parts you want us to solve. Let the index i denote the state variables corresponding to ith state and let the index ij denote the path variables corresponding to the transformation i to j. Let the monoatomic gas’s number of moles and adiabatic index be denoted by n and γ, respectively. a) For process 1 to 2, determine the PV-work and the change in the internal energy from the standard formulas as follows: W12=P1V2-V1=2P03V0-V0=4P0V0ΔE12=32P1V2-V1=322P03V0-V0=6P0V0Use the first thermodynamics law and determine the heat transferred for this process as follows: Q12=ΔE12+W12=6P0V0+4P0V0=10P0V0For the adiabatic process 2 to 3, the heat transferred is zero. Determine the volume (V3) and the change in the internal energy from their standard formulas as follows: P2V2γ=P3V3γV3=2P0P01/γ3V0=23/53V0 ∵γ=53ΔE23=32P3V3-P2V2=32P023/53V0-2P03V0=-2.18P0V0Use the first thermodynamics law and determine the work done in this process as follows: Q23=ΔE23+W230=-2.18P0V0+W23W23=2.18P0V0For process 3 to 4, determine the PV-work and the change in the internal energy from the standard formulas as follows: W34=P3V4-V3=P0V0-23/53V0=1-23/53P0V0ΔE34=32P3V4-V3=32P0V0-23/53V0=321-23/53P0V0Use the first thermodynamics law and determine the heat transferred for this process as follows: Q34=ΔE34+W34=1-23/53P0V0+321-23/53P0V0=-8.87P0V0For process 4 to 1, the PV-work is zero. Determine the change in the internal energy and the heat transferred from the standard formulas as follows: ΔE41=32V4P1-P4=32V02P0-P0=1.5P0V0Q41=ΔE41+W41=1.5P0V0+0=1.5P0V0Hence, the given table can be completed as follows: Hence, the net work done (Wnet) is 2.63P0V0 and the net heat input (Qin) is 11.5 P0V0.This machine’s efficiency (η) is the ratio of the work output and the heat absorbed. Evaluate it as follows: η=WnetQin=2.63P0V011.5P0V0=0.23 or 22.87%

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A heat engine uses an ideal gas of N monatomic particles as its working substance. The engine runs on the following four-step cycle. dyamice 2 2po Transformation 1-2 is isobaric Transformation 2-3 is adiabatic Transformation 3-4 is isobaric Transformation 4-1 is isochoric Po 4 V Vo 3V. Questi 2s for a) Find the efficiency of this engine. You may find it helpful to organize your work as follows: Step 3.

A heat engine uses an ideal gas of N monatomic particles as its working substance. The engine runs on the following four-step cycle. dyamice 2 2po Transformation 1-2 is isobaric Transformation 2-3 is adiabatic Transformation 3-4 is isobaric Transformation 4-1 is isochoric Po 4 V Vo 3V. Questi 2s for a) Find the efficiency of this engine. You may find it helpful to organize your work as follows: Step 3.

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WS T5 (rev. 3.0)
Page 29
A heat engine uses an ideal gas of N
monatomic particles as its working substance.
The engine runs on the following four-step
cycle.
iStmica
2po
Transformation 1+2 is isobaric
Transformation 2-3 is adiabatic
Transformation 3→4 is isobaric
Transformation 4 1 is isochoric
Po
3
4
V
Vo
3V.
Questions
a) Find the efficiency of this engine. You may find it helpful to organize your work as follows:
Step
1- 2
2→ 3
AEnet
W
Q
3 -4
41
Wnet
Qin
b) Where in this cycle does the gas reach its
highest and lowest temperatures? Find these
extreme temperatures. (Your answers shouldabapossible? *
be in terms of po, Vo, and N.)
d) Are your answers consistent with the fact that
the Carnot engine is the most efficient engine
c) What would be the efficiency of a Carnot
engine operating between these two
temperatures?
•...

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