Lesson test: Cycles and the mean temperature

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Cycles and the mean temperature

1.[2p]
A cycle receives $2921$ kJ/kg and rejects $1944$ kJ/kg. What is its thermal efficiency?

CorrectNot quite: 0.334

2.[2p]
A gas turbine's compressor absorbs $311.8$ kJ/kg and its turbine delivers $715.3$ kJ/kg. What is the back work ratio?

CorrectNot quite: 0.436

3.[2p]
Why does the back work ratio matter as much as thermal efficiency?

At a high back work ratio a small slip in either machine wipes out a large share of the net output

Correct

It sets the maximum temperature the cycle can reach

The answer is: At a high back work ratio a small slip in either machine wipes out a large share of the net output

It determines the mass flow rate needed for a given power

The answer is: At a high back work ratio a small slip in either machine wipes out a large share of the net output

It is what the Carnot bound actually limits

The answer is: At a high back work ratio a small slip in either machine wipes out a large share of the net output

4.[3p]
A cycle adds $2921$ kJ/kg of heat with an entropy rise of $6.0958$ kJ/(kg K). What is its mean temperature of heat addition, in kelvin?

CorrectNot quite: 479

5.[2p]
That cycle rejects heat at $319$ K. What efficiency does $1 - T_{L} / {\overline{T}}_{H}$ predict?

CorrectNot quite: 0.334

6.[2p]
For a cycle whose heat rejection is at a single temperature, the thermal efficiency is exactly Carnot's evaluated at the mean temperature of heat addition.

True

Correct

False

The answer is: True

7.[3p]
Why is a Carnot vapour cycle never built?

Select all that apply

Isothermal heat addition confines it to the dome, capping the top temperature at the critical temperature

Correct

The expansion ends deep in the wet region, eroding turbine blades

Correct

The compression stage would have to handle a two-phase mixture

Correct

The condensation must be stopped at one precise quality

Correct

It violates the Second Law, since no cycle can be reversible

The answer is: Isothermal heat addition confines it to the dome, capping the top temperature at the critical temperature, The expansion ends deep in the wet region, eroding turbine blades, The compression stage would have to handle a two-phase mixture, The condensation must be stopped at one precise quality

8.[3p]
Match each Rankine repair to the Carnot objection it answers.

Condense completely to liquid
Pump instead of compress
Add heat at constant pressure
Superheat outside the dome

exhaust is drier
back work ratio falls
peak temperature is not capped
no two-phase compressor

Show the answer

Condense completely to liquid: no two-phase compressor Pump instead of compress: back work ratio falls Add heat at constant pressure: peak temperature is not capped Superheat outside the dome: exhaust is drier

9.[2p]
The heat addition in the baseline cycle spends $28$ per cent of its energy warming subcooled water. What does that do?

It drags the mean temperature of heat addition down, and with it the efficiency

Correct

It raises the back work ratio

The answer is: It drags the mean temperature of heat addition down, and with it the efficiency

It lowers the condenser pressure

The answer is: It drags the mean temperature of heat addition down, and with it the efficiency

It has no effect, since that heat is recovered in the condenser

The answer is: It drags the mean temperature of heat addition down, and with it the efficiency

1.[2p] A cycle receives 2921 kJ/kg and rejects 1944 kJ/kg. What is its thermal efficiency?

2.[2p] A gas turbine's compressor absorbs 311.8 kJ/kg and its turbine delivers 715.3 kJ/kg. What is the back work ratio?

3.[2p] Why does the back work ratio matter as much as thermal efficiency?

4.[3p] A cycle adds 2921 kJ/kg of heat with an entropy rise of 6.0958 kJ/(kg K). What is its mean temperature of heat addition, in kelvin?

5.[2p] That cycle rejects heat at 319 K. What efficiency does 1−TL/T‾H predict?

6.[2p] For a cycle whose heat rejection is at a single temperature, the thermal efficiency is exactly Carnot's evaluated at the mean temperature of heat addition.

7.[3p] Why is a Carnot vapour cycle never built?

8.[3p] Match each Rankine repair to the Carnot objection it answers.

9.[2p] The heat addition in the baseline cycle spends 28 per cent of its energy warming subcooled water. What does that do?

1.[2p]
A cycle receives $2921$ kJ/kg and rejects $1944$ kJ/kg. What is its thermal efficiency?

2.[2p]
A gas turbine's compressor absorbs $311.8$ kJ/kg and its turbine delivers $715.3$ kJ/kg. What is the back work ratio?

3.[2p]
Why does the back work ratio matter as much as thermal efficiency?

4.[3p]
A cycle adds $2921$ kJ/kg of heat with an entropy rise of $6.0958$ kJ/(kg K). What is its mean temperature of heat addition, in kelvin?

5.[2p]
That cycle rejects heat at $319$ K. What efficiency does $1 - T_{L} / {\overline{T}}_{H}$ predict?

6.[2p]
For a cycle whose heat rejection is at a single temperature, the thermal efficiency is exactly Carnot's evaluated at the mean temperature of heat addition.

7.[3p]
Why is a Carnot vapour cycle never built?

8.[3p]
Match each Rankine repair to the Carnot objection it answers.

9.[2p]
The heat addition in the baseline cycle spends $28$ per cent of its energy warming subcooled water. What does that do?