Air Standard Cycle MCQ Quiz in বাংলা - Objective Question with Answer for Air Standard Cycle - বিনামূল্যে ডাউনলোড করুন [PDF]

As R for a gas is constant

So \({C_p} - {C_v} = R = C_p' - C_v'\)

\(\Rightarrow C_p' = \left( {{C_p} - {C_v}} \right) + C_v'\)

\(= \left( {{C_p} - {C_v}} \right) + 1.01{C_v}\)

\(= 1.4{C_v} - {C_v} + 1.01{C_v} \Rightarrow C_p' = 1.41{C_v}\)

\(\gamma ' = \frac{{C_p'}}{{C_v'}} = \frac{{1.41{C_v}}}{{1.01{C_v}}} = 1.396\)

\(\eta = 1 - \frac{1}{{{{\left( r \right)}^{\gamma - 1}}}} = 1 - \frac{1}{{{{\left( 7 \right)}^{1.4 - 1}}}} = 0.5408\)

\({\eta ^1} = 1 - \frac{1}{{{{\left( r \right)}^{\gamma ' - 1}}}} = 1 - {\left( {\frac{1}{7}} \right)^{1.396 - 1}} = 0.5372\)

\(\therefore \% \;charge\;in\;efficiency\left( \eta \right) = \frac{{0.5408 - 0.5372}}{{0.5408}} \times 100\)

= 0.666%

Explanation:

The accurate analysis of internal combustion engine processes is very complicated, in order to understand them air standard cycles are proposed to analyze the performance of the real cycle.

Note: Air-standard cycle, is based on the following assumptions :

i) The working medium is assumed to be a perfect gas and follows the relation pV = mRT or p = ρRT

ii) There is no change in the mass of the working medium

iii) All the processes that constitute the cycle are reversible

iv) Heat is assumed to be supplied from a constant high-temperature source and not from chemical reactions during the cycle

v) The working medium has constant specific heats throughout the cycle

For same values of peak pressure and temperature. Diesel cycle is most efficient and Otto cycle is least. Efficiency of dual cycle lies in between.

η_Diesel > η_Dual > η_Otto

And for same compression ratio and heat rejection or heat addition,

ηOtto > ηDual > ηDiesel

Stirling cycle and Ericsson cycle are the modified forms of the Carnot cycle.

A Stirling cycle consists of two reversible isothermal and two reversible constant volume (isochoric) processes.

\({\eta _{Stirling}} = \frac{{{T_3} - {T_1}}}{{{T_3}}}\)

Which is the same, as Carnot efficiency.

Additional InformationWhereas an Ericsson cycle consists of two reversible isothermal and two reversible constant pressure (isobaric) process.

\(\eta _{ericsson}=1-\frac{T_1}{T_3}\)

which is the same as Carnot efficiency

Stirling and Ericsson Cycles:

• The ideal Otto and Diesel cycles are internally reversible, but not totally reversible.
• Hence their efficiencies will always be less than that of Carnot efficiency.
• For a cycle to approach a Carnot cycle, heat addition and heat rejection must take place isothermally.
• Stirling and Ericsson cycles comprise of isothermal heat addition and heat rejection.
• Both these cycles also have a regeneration process.
• Regeneration, a process during which heat is transferred to a thermal energy storage device (called a regenerator) during one part of the cycle and is transferred back to the working fluid during another part of the cycle.

Explanation:

Carnot cycle:

The ideal reversible cycle that has the highest possible efficiency among all heat engines is called the Carnot cycle.

Carnot cycle is one of the best-known reversible cycles. The Carnot cycle is composed of four reversible processes.

• Reversible Isothermal Expansion (process 1-2)
• Reversible adiabatic expansion (process 2-3)
• Reversible isothermal compression (process 3-4)
• Reversible adiabatic compression (process 4-1)

Fig. P-V and T-S diagrams of Carnot Cycle

The Carnot cycle consists of two isothermal and two isentropic processes.

Explanation:

The Carnot cycle consists of 4 processes

• 1-2 isothermal heat addition
• 2-3 reversible adiabatic expansion
• 3-4 isothermal heat rejection
• 4-1 reversible adiabatic compression

A cycle is said to be reversible only when each process in a cycle is reversible.

The Carnot cycle consists of 2 isothermal and 2 adiabatic processes.

Explanation:

The Stirling cycle is a thermodynamic cycle that describes the general class of Stirling devices. This includes the original Stirling engine that was invented, developed and patented in 1816 by Robert Stirling with help from his brother.

• The Stirling cycle bears a double-effect piston and cylinder arrangement.
• A regenerator porous matrix is mounted inside the arrangement.
• The working fluid can be air, helium, nitrogen, hydrogen, CO2, etc.
• The main processes within the Stirling cycle are written as follows

1. Process 1-2: Isothermal compression: The working fluid is compressed isothermally while space discharges the heat to the heat sink. Therefore, the temperature of the heat sink is increased.
2. Process 2-3: Isochoric regeneration (heat addition): Heating occurs at the regenerator under constant volume. The temperature of the working fluid increases from TL to TH.
3. Process 3-4: Isothermal expansion: The working fluid expands isothermally while space is heated externally by the heat source. At this stage, the engine produces useful work.
4. Process 4-1: Isochoric regeneration (heat rejection): Cooling occurs at regeneration component at constant volume. Regenerator absorbs heat from the working fluid. The temperature of the working fluid reduces from TH to TL.

∴ Option (4) is the correct Answer.

Explanation:

Lenoir cycle:

The Lenoir cycle is an idealized thermodynamic cycle often used to model a pulse jet engine. It is based on the operation of an engine patented by Jean Joseph Etienne Lenoir. This engine is the first commercially produced internal combustion engine.

Where,

Constant volume heat addition (1–2)

Isentropic expansion (2–3)

Constant pressure heat rejection (3–1)

The below plot is the comparison of the efficiencies of the Otto cycle and the Lenoir cycle at different compression ratios.

Explanation:

Diesel cycle:

​

Processes in compression engine (diesel cycle) are:

1. Process 1-2: Reversible adiabatic compression
2. Process 2-3: Constant pressure heat addition
3. Process 3-4: Reversible adiabatic expansion
4. Process 4-1: Constant volume of heat rejection

Hence an air-standard diesel cycle consists of one constant pressure, one constant volume and two adiabatic processes.

Additional Information

Otto cycle:

The air-standard-Otto cycle is the idealized cycle for the spark-ignition internal combustion engines.

Otto cycle is the one that has two constant volume heat transfer processes and two adiabatic work transfer processes.

The Otto cycle 1-2-3-4 consists of the following four processes:

• Process 1-2: Reversible adiabatic compression of air
• Process 2-3: Heat addition at constant volume
• Process 3-4: Reversible adiabatic expansion of air
• Process 4-1: Heat rejection at constant volume
   

• During constant volume process heat addition and heat, rejection takes place and no work transfer.
• During the adiabatic processes [compressions/expansion] only work transfer taken place but no heat transfer occurs.​

Dual cycle 

The Dual Cycle also called a mixed cycle or limited pressure cycle is a compromise between Otto and Diesel cycles.

The dual cycle is a thermodynamic cycle that combines the Otto cycle and the Diesel cycle. In this cycle, the heat addition occurs partly at constant volume and partly at constant pressure.

Different processes in the dual cycles are given below:

Process 1-2: Reversible adiabatic compression.

Process 2-3: Constant volume heat addition.

Process 3-4: Constant pressure heat addition.

Process 4-5: Reversible adiabatic expansion.

Process 5-1: Constant volume heat rejection.

Explanation:

• The volumetric efficiency of a compressor is given by:
• \({\eta _v} = \frac{{actual\;volume\;of\;air\;drawn\;in}}{{swept\;volume}}\)
• ${\eta _v} = 1 + c - c{\left( {\frac{{{P_d}}}{{{P_s}}}} \right)^{\frac{1}{n}}}$
• \({\eta _v} = 1 - c\left[ {{{\left( {\frac{{{P_d}}}{{{P_s}}}} \right)}^{\frac{1}{n}}} - 1} \right]\)..........(1)
• where c is clearance ratio, \(c = \frac{{{V_c}}}{{{V_s}}}\)
• V_c is clearance volume and V_s is swept volume, P_d is delivery pressure and P_s is suction pressure.
• From eq. 1 it is very clear that η_v is inversely proportional to clearance ratio, c which is directly proportional to clearance volume V_c.
• By increasing clearance volume, the clearance ratio will increase which results in a decrease in volumetric efficiency as is clear from equation 1.
• V_c↑ ⇒ c↑ ⇒ η_v↓ 
• That’s why clearance volume is kept at a minimum to increase the maximum amount of air drawn or sucked in to produce more power and consequently more torque in diesel engines and more speed in petrol engines.

Important Points 

• Clearance volume should not be so less that the piston should hit the cylinder head when running under no-load condition (i.e. when there is minimum resistance to its motion). So there is an optimum balance between the two while designing the piston-cylinder arrangement.