1.An aircraft engine takes in an amount 9100 J of heat and discards an amount 66

Question

1.An aircraft engine takes in an amount 9100 J of heat and discards an amount 6600 J each cycle

a)What is the mechanical work output of the engine during one cycle?

b)What is the thermal efficiency of the engine?

Express your answer as a percentage.

The idealized cycle shown is known as the Otto cycle. (Figure 1) Suppose an engine is executing this Otto cycle, using a gas (not necessarily ideal) as its working substance. From state A to state B, the gas is allowed to expand adiabatically. (An adiabatic process is one in which no heat is added to, or given off by, the working gas.) The gas is then cooled at constant volume until it reaches state C, at which point it is adiabatically compressed to state D. Finally, it is heated at constant volume until it returns to state A.

The pressure and volume of the gas in state A are pAand VA respectively. The pressure and volume of the gas in state C are pC and VC respectively.

Part A

How much heat QAB is added to the gas as it proceeds from state A to state B?

Express your answer in terms of any needed variables from the problem introduction.

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Part B

How much heat QCD is given up by the gas as it proceeds from state C to state D?

Express your answer in terms of any needed variables from the problem introduction.

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Part C

What is U, the change in the gas's internal energy after a complete cycle?

Express your answer in terms of any needed variables from the problem introduction.

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Part D

Suppose you want positive work to be done by the gas. In which direction should the Otto cycle be run?

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Figure 1 of 1

The idealized cycle shown is known as the Otto cycle. (Figure 1) Suppose an engine is executing this Otto cycle, using a gas (not necessarily ideal) as its working substance. From state A to state B, the gas is allowed to expand adiabatically. (An adiabatic process is one in which no heat is added to, or given off by, the working gas.) The gas is then cooled at constant volume until it reaches state C, at which point it is adiabatically compressed to state D. Finally, it is heated at constant volume until it returns to state A.

The pressure and volume of the gas in state A are pAand VA respectively. The pressure and volume of the gas in state C are pC and VC respectively.

Part A

How much heat QAB is added to the gas as it proceeds from state A to state B?

Express your answer in terms of any needed variables from the problem introduction.

Hints

QAB=

SubmitMy AnswersGive Up

Part B

How much heat QCD is given up by the gas as it proceeds from state C to state D?

Express your answer in terms of any needed variables from the problem introduction.

Hints

QCD=

SubmitMy AnswersGive Up

Part C

What is U, the change in the gas's internal energy after a complete cycle?

Express your answer in terms of any needed variables from the problem introduction.

Hints

U=

SubmitMy AnswersGive Up

Part D

Suppose you want positive work to be done by the gas. In which direction should the Otto cycle be run?

clockwise (A to B to C to D to A) counterclockwise (A to D to C to B to A)

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Figure 1 of 1

adiabatic expansion adiabatic compression

Explanation / Answer

1)a) work done = heat in - heat out
= 9100 -6600 = 2500 J per cycle.

b) the efficiency = work out / heat in
= 2500/9100
= 0.275 or 27.5%

2) a)  QAB=0

b) QCD=0

c) U= 0

d) clockwise (A to B to C to D to A)

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