Mechanical
The Rankine cycle is primarily used in:
- Steam power plants
- SI engines
- CI engines
- Gas turbines only
Explanation:
- The Rankine cycle is the basic thermodynamic cycle used for steam power generation. Water and steam act as the working fluid.
A simple Rankine cycle consists of how many ideal processes?
- Four
- Three
- Five
- Six
Explanation:
- The four processes are isentropic pumping, constant-pressure heat addition in the boiler, isentropic expansion in the turbine, and constant-pressure heat rejection in the condenser.
In a simple Rankine cycle, the working fluid is:
- Water/steam
- Air only
- Gasoline
- Diesel fuel
Explanation:
- Water is used as the working fluid in the conventional Rankine steam cycle because it is readily available and has suitable thermodynamic properties.
Which component increases the pressure of water in a simple Rankine cycle?
- Pump
- Turbine
- Condenser
- Boiler
Explanation:
- The pump raises the pressure of condensate from condenser pressure to boiler pressure before heat addition.
Which component of a Rankine cycle produces the major portion of the net work output?
- Turbine
- Pump
- Condenser
- Boiler
Explanation:
- The turbine expands high-pressure steam and produces a large amount of work. Pump work is relatively small compared with turbine work.
Which component rejects heat in a simple Rankine cycle?
- Condenser
- Boiler
- Pump
- Turbine
Explanation:
- The condenser rejects heat from the exhaust steam and converts it back into liquid water.
In the ideal Rankine cycle, the pump process is:
- Isentropic compression
- Isothermal compression
- Constant-pressure expansion
- Constant-volume compression
Explanation:
- In the ideal Rankine cycle, the pump is assumed to operate reversibly and adiabatically, making the process isentropic.
In the ideal Rankine cycle, the turbine process is:
- Isentropic expansion
- Isothermal expansion
- Constant-volume expansion
- Constant-pressure compression
Explanation:
- The ideal turbine expansion is reversible and adiabatic, so entropy remains constant.
Heat addition in the simple Rankine cycle occurs in the:
- Boiler
- Condenser
- Pump
- Turbine
Explanation:
- The boiler supplies heat to the high-pressure feedwater, converting it into steam and usually superheating it before turbine expansion.
In the ideal Rankine cycle, heat rejection occurs approximately at:
- Constant pressure
- Constant volume
- Constant entropy
- Constant temperature throughout the entire condenser process
Explanation:
- Condensation in the ideal Rankine cycle occurs at essentially constant pressure. For a pure substance in the two-phase region, it also occurs at constant saturation temperature.
Which sequence correctly represents the four processes of a simple Rankine cycle?
- Pump → Boiler → Turbine → Condenser
- Boiler → Pump → Condenser → Turbine
- Turbine → Boiler → Pump → Condenser
- Condenser → Turbine → Boiler → Pump
Explanation:
- The condensate is pumped to boiler pressure, heated in the boiler, expanded in the turbine, and finally condensed in the condenser.
On a P-V diagram, the pumping process of an ideal Rankine cycle is represented approximately by:
- A nearly vertical compression process
- A horizontal expansion process
- A horizontal compression process
- A constant-temperature expansion curve
Explanation:
- Liquid water has a very small change in specific volume during pumping, so the pump process appears nearly vertical on a P-V diagram.
On a T-S diagram, the ideal pump process is represented by:
- A vertical line
- A horizontal line
- A circular curve
- A constant-volume curve
Explanation:
- For an ideal pump, the process is isentropic, so entropy remains constant and the process is vertical on a T-S diagram.
On a T-S diagram, the ideal turbine expansion is represented by:
- A vertical downward line
- A horizontal line
- A vertical upward line
- A constant-volume curve
Explanation:
- The ideal turbine process is isentropic. During expansion, temperature decreases while entropy remains constant.
On a T-S diagram, the boiler heat-addition process generally moves:
- Toward higher temperature and higher entropy
- Toward lower temperature and lower entropy
- Only vertically downward
- Only at constant entropy
Explanation:
- Heat addition causes the working fluid to gain energy and, for the boiler process, entropy generally increases from the compressed-liquid state toward the steam state.
On a T-S diagram, the condenser process of a simple Rankine cycle is represented approximately by:
- A heat-rejection path toward lower entropy
- An isentropic upward path
- A constant-volume expansion
- An isentropic compression only
Explanation:
- During condensation, heat is rejected and the steam changes toward liquid, causing entropy to decrease.
The area under a reversible process curve on a T-S diagram represents:
- Heat transfer
- Pressure
- Specific volume
- Specific work in every process
Explanation:
- For a reversible process, δq = T ds. Therefore, the area under the curve on a T-S diagram represents heat transfer.
The area enclosed by an ideal Rankine cycle on a T-S diagram represents:
- Net heat transfer and hence net work per unit mass
- Pump work only
- Condenser heat rejection only
- Boiler pressure
Explanation:
- For a complete cycle, Δu = 0. Therefore, net heat transfer equals net work. On a T-S diagram, the enclosed area represents the net heat transfer for reversible processes.
In an h-s diagram, which axis represents entropy?
- Horizontal axis
- Vertical axis
- Both axes
- Neither axis
Explanation:
- The Mollier or h-s diagram plots specific enthalpy h on the vertical axis and specific entropy s on the horizontal axis.
The Mollier diagram is also known as the:
- h-s diagram
- P-V diagram
- T-V diagram
- P-T diagram
Explanation:
- A Mollier chart is a plot of specific enthalpy against specific entropy and is widely used for steam turbine calculations.
On an h-s diagram, an ideal isentropic turbine expansion is represented by:
- A vertical downward line
- A horizontal line
- A vertical upward line
- A constant-pressure curve only
Explanation:
- Since entropy remains constant during ideal turbine expansion, s is constant. With entropy on the horizontal axis, the process is vertical and enthalpy decreases.
The turbine work in an ideal Rankine cycle is:
- Wt = h3 − h4
- Wt = h4 − h3
- Wt = h2 − h1
- Wt = h1 − h4
Explanation:
- For steady-flow adiabatic turbine operation with negligible kinetic and potential energy changes, turbine work per unit mass equals the enthalpy drop, h3 − h4.
The pump work for an ideal Rankine cycle is:
- Wp = h2 − h1
- Wp = h1 − h2
- Wp = h3 − h4
- Wp = h4 − h1
Explanation:
- The pump increases the enthalpy of the feedwater from state 1 to state 2, so pump work is h2 − h1.
The net work output of a Rankine cycle is:
- Wnet = Wt − Wp
- Wnet = Wt + Wp
- Wnet = Wp − Wt
- Wnet = Wt/Wp
Explanation:
- The turbine produces work while the pump consumes work. Therefore, net work output is turbine work minus pump work.
The heat supplied to the working fluid in a simple Rankine cycle is:
- Qin = h3 − h2
- Qin = h2 − h3
- Qin = h4 − h1
- Qin = h1 − h4
Explanation:
- Heat is added in the boiler as the fluid moves from state 2 to state 3. Therefore, qin = h3 − h2.
The heat rejected in the condenser is:
- Qout = h4 − h1
- Qout = h1 − h4
- Qout = h3 − h2
- Qout = h2 − h1
Explanation:
- During condensation, enthalpy decreases from h4 to h1. Therefore, the magnitude of heat rejected is h4 − h1.
The thermal efficiency of a Rankine cycle is defined as:
- η = Wnet/Qin
- η = Qin/Wnet
- η = Wp/Wt
- η = Qout/Qin
Explanation:
- Thermal efficiency is the ratio of net work output to heat supplied: η = Wnet/Qin.
Considering pump work, the thermal efficiency of a simple Rankine cycle is:
- η = [(h3 − h4) − (h2 − h1)]/(h3 − h2)
- η = (h3 − h4)/(h3 − h2)
- η = (h2 − h1)/(h3 − h4)
- η = (h3 − h2)/(h3 − h4)
Explanation:
- When pump work is included, net work is turbine work minus pump work. Hence η = [(h3 − h4) − (h2 − h1)]/(h3 − h2).
If pump work is neglected, the thermal efficiency of the Rankine cycle becomes:
- η = (h3 − h4)/(h3 − h2)
- η = (h2 − h1)/(h3 − h4)
- η = (h4 − h1)/(h3 − h2)
- η = (h3 − h2)/(h3 − h4)
Explanation:
- When pump work is neglected, net work is approximated as turbine work. Thus η ≈ Wt/Qin.
Neglecting pump work in a Rankine cycle generally makes the calculated thermal efficiency:
- Slightly higher than the actual value including pump work
- Lower than the actual value
- Exactly zero
- Exactly equal in all cases
Explanation:
- Pump work is an input to the cycle. Neglecting it makes the net work output appear slightly larger, so the calculated efficiency is slightly higher.
The pump work in a simple Rankine cycle is generally much smaller than turbine work because:
- Water in the liquid state has very low specific volume
- Steam has zero enthalpy
- The turbine does no work
- The condenser supplies work to the pump
Explanation:
- For an incompressible liquid, pump work can be approximated by v(P2 − P1). Since liquid water has small specific volume, pump work is relatively small.
For an ideal pump handling an incompressible liquid, pump work is approximately:
- Wp ≈ v(P2 − P1)
- Wp ≈ P/v
- Wp ≈ v/(P2 − P1)
- Wp ≈ P2/P1
Explanation:
- For an incompressible liquid, the specific pump work is approximately vΔP, where v is specific volume and ΔP is the pressure rise.
The Rankine cycle differs from the Carnot vapor cycle mainly because:
- Compression in the Rankine cycle occurs in the liquid phase using a pump
- Rankine cycle has no condenser
- Rankine cycle has no heat rejection
- Rankine cycle uses air as the working fluid
Explanation:
- In the Rankine cycle, the working fluid is condensed to liquid before compression. Pumping a liquid requires much less work than compressing a vapor.
One major advantage of using a pump instead of a compressor in a Rankine cycle is:
- Much lower compression work
- Higher fuel consumption
- Higher condenser pressure
- Elimination of the boiler
Explanation:
- Compressing liquid water requires much less work than compressing steam over the same pressure range, which improves the practicality of the Rankine cycle.
In the simple Rankine cycle, the fluid entering the pump is ideally:
- Saturated liquid
- Superheated steam
- Wet steam with high quality
- Dry air
Explanation:
- Ideally, the condenser produces saturated liquid at the condenser pressure before the pump raises its pressure.
The quality of steam entering the turbine is important because:
- Excessive moisture can cause turbine blade erosion
- Moisture always increases turbine efficiency
- Moisture eliminates heat rejection
- Steam quality has no effect on turbine operation
Explanation:
- High moisture content in the later stages of a steam turbine can cause erosion of turbine blades and reduce performance.
Superheating steam before turbine expansion generally:
- Increases cycle efficiency and reduces moisture at turbine exit
- Always decreases efficiency
- Eliminates the need for a condenser
- Eliminates pump work
Explanation:
- Superheating increases the average temperature of heat addition and generally improves thermal efficiency. It also tends to increase the dryness fraction at turbine exhaust.
Increasing the boiler pressure in a simple Rankine cycle, with other conditions suitably fixed, generally:
- Can increase thermal efficiency
- Always reduces thermal efficiency to zero
- Eliminates turbine work
- Eliminates condenser heat rejection
Explanation:
- Increasing boiler pressure can raise the average temperature of heat addition and improve Rankine-cycle efficiency, although practical limits and turbine-exhaust moisture must also be considered.
Reducing condenser pressure in a Rankine cycle generally:
- Increases turbine work and can increase thermal efficiency
- Always decreases turbine work
- Eliminates pump work
- Eliminates the boiler
Explanation:
- A lower condenser pressure increases the turbine expansion ratio and generally increases turbine work and cycle efficiency, subject to practical limitations.
The ideal Rankine cycle is commonly represented by four states numbered in sequence as:
- 1: condenser exit, 2: pump exit, 3: boiler exit, 4: turbine exit
- 1: turbine exit, 2: condenser exit, 3: pump exit, 4: boiler exit
- 1: boiler exit, 2: turbine exit, 3: condenser exit, 4: pump exit
- 1: pump exit, 2: turbine exit, 3: condenser exit, 4: boiler exit
Explanation:
- The conventional numbering starts at the condenser outlet: 1–2 pumping, 2–3 boiler heat addition, 3–4 turbine expansion and 4–1 condensation.
On an h-s diagram, the enthalpy drop across the ideal turbine is represented by:
- h3 − h4
- h4 − h3
- h2 − h1
- h1 − h2
Explanation:
- During turbine expansion, enthalpy decreases from h3 to h4. The difference represents ideal turbine work per unit mass.
Which process in the Rankine cycle occurs inside the condenser?
- 4–1
- 1–2
- 2–3
- 3–4
Explanation:
- Process 4–1 is constant-pressure heat rejection and condensation in the ideal simple Rankine cycle.
Which process in the Rankine cycle occurs inside the boiler?
- 2–3
- 1–2
- 3–4
- 4–1
Explanation:
- Process 2–3 represents heat addition in the boiler, including heating of the feedwater, evaporation and possible superheating.
Which process in the Rankine cycle occurs inside the turbine?
- 3–4
- 1–2
- 2–3
- 4–1
Explanation:
- High-pressure steam expands through the turbine during process 3–4 and produces work.
Which process in the Rankine cycle occurs inside the pump?
- 1–2
- 2–3
- 3–4
- 4–1
Explanation:
- The pump raises the pressure of the condensed liquid during process 1–2.
If the pump work is neglected, the net work of the Rankine cycle is approximately equal to:
- Turbine work
- Pump work
- Condenser heat rejection
- Boiler heat input
Explanation:
- Since Wp is neglected, Wnet = Wt − Wp ≈ Wt.
For the ideal Rankine cycle, the entropy at the turbine inlet and turbine exit is:
- Equal
- Always zero
- Always doubled
- Unrelated
Explanation:
- Ideal turbine expansion is isentropic, so s3 = s4.
For the ideal Rankine cycle, the entropy at the pump inlet and pump exit is:
- Approximately equal
- Always zero at the inlet
- Always doubled
- Always reduced to half
Explanation:
- The ideal pump process is isentropic, so s1 = s2 under the idealized model.
The principal objective of the Rankine cycle is to convert:
- Heat energy into useful mechanical work
- Mechanical work into heat only
- Electricity directly into steam
- Pressure directly into fuel
Explanation:
- A steam power plant uses the Rankine cycle to convert heat supplied in the boiler into turbine work and ultimately electrical power.
Which change generally increases the average temperature of heat addition in a Rankine cycle?
- Superheating the steam
- Increasing condenser heat rejection
- Increasing pump outlet liquid volume only
- Reducing boiler temperature
Explanation:
- Superheating raises the temperature at which part of the heat is added, increasing the average temperature of heat addition and generally improving cycle efficiency.