Lesson test: The Rankine cycle

The Rankine cycle

1.[2p]
Put the four processes of the Rankine cycle in the order the fluid meets them, starting at the condenser outlet.

Isentropic expansion through the turbine
Isentropic compression through the feed pump
Constant-pressure heat rejection in the condenser
Constant-pressure heat addition in the boiler

Show the answer

d, a, b, c

2.[2p]
Water at $10$ kPa with $v_{f} = 0.001010$ m³/kg is pumped to $3$ MPa. What is the ideal pump work, in kJ/kg?

CorrectNot quite: 3.02

3.[2p]
Steam at $3$ MPa and $350$ degrees Celsius has $h = 3116.1$ kJ/kg. The feed water enters the boiler at $194.83$ kJ/kg. What heat does the boiler supply, in kJ/kg?

CorrectNot quite: 2921

4.[2p]
The ideal cycle delivers $980.0$ kJ/kg of turbine work and absorbs $3.02$ kJ/kg of pump work on a heat input of $2921$ kJ/kg. What is its thermal efficiency?

CorrectNot quite: 0.334

5.[2p]
With a turbine of isentropic efficiency $0.87$ and a pump of $0.85$ , the same cycle gives $849.0$ kJ/kg net on $2920.7$ kJ/kg of heat. What is the thermal efficiency now?

CorrectNot quite: 0.291

6.[3p]
Raising the condenser pressure from $10$ to $20$ kPa costs the cycle about two efficiency points. Why is such a small pressure change so expensive?

It raises the temperature at which all the heat is rejected, shortening the turbine's expansion

Correct

It raises the pump work substantially

The answer is: It raises the temperature at which all the heat is rejected, shortening the turbine's expansion

It makes the turbine exhaust wetter, eroding the blades

The answer is: It raises the temperature at which all the heat is rejected, shortening the turbine's expansion

It lowers the mean temperature of heat addition

The answer is: It raises the temperature at which all the heat is rejected, shortening the turbine's expansion

7.[2p]
Fitting a worse turbine leaves the condenser duty unchanged, since energy not taken by the shaft simply never enters the cycle.

True

The answer is: False

False

Correct

8.[3p]
Match each departure of a real plant from the ideal cycle to its effect.

Pressure drop in boiler tubes
Subcooling of condensate
Air in-leakage to the condenser
Combustion gas at 1800 K

heat rejected then paid for again
the plant's largest irreversibility
heat transfer destroyed on tubes
lower turbine inlet pressure

Show the answer

Pressure drop in boiler tubes: lower turbine inlet pressure Subcooling of condensate: heat rejected then paid for again Air in-leakage to the condenser: heat transfer destroyed on tubes Combustion gas at 1800 K: the plant's largest irreversibility

9.[3p]
A plant on the real cycle produces $849.0$ kJ/kg net and rejects $2071.7$ kJ/kg. At an output of $100$ MW, what is the condenser duty, in MW?

CorrectNot quite: 244

1.[2p] Put the four processes of the Rankine cycle in the order the fluid meets them, starting at the condenser outlet.

2.[2p] Water at 10 kPa with vf=0.001010 m³/kg is pumped to 3 MPa. What is the ideal pump work, in kJ/kg?

3.[2p] Steam at 3 MPa and 350 degrees Celsius has h=3116.1 kJ/kg. The feed water enters the boiler at 194.83 kJ/kg. What heat does the boiler supply, in kJ/kg?

4.[2p] The ideal cycle delivers 980.0 kJ/kg of turbine work and absorbs 3.02 kJ/kg of pump work on a heat input of 2921 kJ/kg. What is its thermal efficiency?

5.[2p] With a turbine of isentropic efficiency 0.87 and a pump of 0.85, the same cycle gives 849.0 kJ/kg net on 2920.7 kJ/kg of heat. What is the thermal efficiency now?

6.[3p] Raising the condenser pressure from 10 to 20 kPa costs the cycle about two efficiency points. Why is such a small pressure change so expensive?

7.[2p] Fitting a worse turbine leaves the condenser duty unchanged, since energy not taken by the shaft simply never enters the cycle.

8.[3p] Match each departure of a real plant from the ideal cycle to its effect.

9.[3p] A plant on the real cycle produces 849.0 kJ/kg net and rejects 2071.7 kJ/kg. At an output of 100 MW, what is the condenser duty, in MW?

1.[2p]
Put the four processes of the Rankine cycle in the order the fluid meets them, starting at the condenser outlet.

2.[2p]
Water at $10$ kPa with $v_{f} = 0.001010$ m³/kg is pumped to $3$ MPa. What is the ideal pump work, in kJ/kg?

3.[2p]
Steam at $3$ MPa and $350$ degrees Celsius has $h = 3116.1$ kJ/kg. The feed water enters the boiler at $194.83$ kJ/kg. What heat does the boiler supply, in kJ/kg?

4.[2p]
The ideal cycle delivers $980.0$ kJ/kg of turbine work and absorbs $3.02$ kJ/kg of pump work on a heat input of $2921$ kJ/kg. What is its thermal efficiency?

5.[2p]
With a turbine of isentropic efficiency $0.87$ and a pump of $0.85$ , the same cycle gives $849.0$ kJ/kg net on $2920.7$ kJ/kg of heat. What is the thermal efficiency now?

6.[3p]
Raising the condenser pressure from $10$ to $20$ kPa costs the cycle about two efficiency points. Why is such a small pressure change so expensive?

7.[2p]
Fitting a worse turbine leaves the condenser duty unchanged, since energy not taken by the shaft simply never enters the cycle.

8.[3p]
Match each departure of a real plant from the ideal cycle to its effect.

9.[3p]
A plant on the real cycle produces $849.0$ kJ/kg net and rejects $2071.7$ kJ/kg. At an output of $100$ MW, what is the condenser duty, in MW?