Multi Pressure Systems MCQ Quiz - Objective Question with Answer for Multi Pressure Systems - Download Free PDF

Explanation:

Cascade Refrigeration System

Definition: A cascade refrigeration system is a specialized type of refrigeration system that uses two or more refrigeration cycles with different refrigerants to achieve very low temperatures. Each cycle operates at different temperature ranges and is connected in series, where the evaporator of one cycle serves as the condenser for the next cycle.

Working Principle: In a cascade refrigeration system, multiple refrigeration circuits are used in stages, each with its own refrigerant that is best suited for the specific temperature range it operates within. The first stage (high-temperature stage) uses a refrigerant with a relatively higher boiling point, which condenses at a temperature that serves as the evaporator temperature for the second stage (low-temperature stage). The second stage uses a refrigerant with a much lower boiling point, capable of achieving extremely low temperatures.

For example, in a two-stage cascade system, the high-temperature stage might use a refrigerant such as R-134a, while the low-temperature stage might use a refrigerant like R-23. The high-temperature stage absorbs heat from the environment and transfers it to the low-temperature stage, where the second refrigerant absorbs the heat and evaporates at a much lower temperature, providing the desired refrigeration effect.

Advantages:

• Ability to achieve extremely low temperatures that are not possible with a single refrigeration cycle.
• Enhanced efficiency and performance by using refrigerants that are optimized for specific temperature ranges.
• Flexibility in selecting refrigerants that are environmentally friendly and suitable for the desired temperature range.

Disadvantages:

• Increased complexity in design and operation due to multiple refrigeration circuits and components.
• Higher initial cost and maintenance requirements compared to single-stage systems.
• Requires precise control and coordination between the different stages to ensure optimal performance.

Applications: Cascade refrigeration systems are commonly used in applications requiring very low temperatures, such as in cryogenics, pharmaceutical industries, and scientific research laboratories.

Analysis of Other Options:

Option 2: A single refrigerant in both cycles

This option is incorrect because a cascade refrigeration system specifically utilizes multiple refrigerants with different boiling points to achieve the desired temperature ranges. Using a single refrigerant in both cycles would not allow the system to reach extremely low temperatures effectively.

Option 3: Only ammonia as a refrigerant

This option is incorrect because while ammonia is a common refrigerant used in various refrigeration systems, a cascade refrigeration system requires multiple refrigerants with different boiling points to operate efficiently. Relying solely on ammonia would not provide the necessary temperature differential between the stages.

Option 4: Only air as a working fluid

This option is incorrect because air is not used as a refrigerant in cascade refrigeration systems. Refrigeration systems typically use refrigerants that undergo phase changes (liquid to vapor and vice versa) to absorb and reject heat. Air does not have the necessary properties to function effectively as a refrigerant in this context.

Concept:

\({\rm{Work\;}} = \frac{{Nn}}{{n - 1}} \times R{T_1} \times {\left( {\frac{{{P_d}}}{{{P_s}}}} \right)^{\frac{{n - 1}}{{Nn}}}} - 1\)

Isothermal work \( = R{T_1}\;ln\;\left( {\frac{{{P_s}}}{{{P_1}}}} \right)\)

\({\eta _{isothermal}} = \frac{{isothermal\;work}}{{polytropic\;work}}\)

Calculation:

Given: P₁ = 90 kPa = P_s, P_d = 4000 kPa, n = 1.31, N = 4

Now,

\({\rm{Compressor\;work\;}} = \frac{{4\; \times \;1.31}}{{0.31}} \times 0.287 \times 300 \times \left[ {{{\left( {\frac{{4000}}{{90}}} \right)}^{\frac{{0.31}}{{4\; \times \;1.31}}}} - 1} \right]\)

∴ Compressor work = 366.253 kJ/kg

Now,

\({\rm{Isothermal\;work}} = 0.287 \times 300 \times ln\left( {\frac{{4000}}{{90}}} \right)\)

∴ Isothermal work = 326.684 kJ/kg

\(\therefore \;{\eta _{isothermal}}\; = \frac{{326.689}}{{366.253}}\;\)

∴ η_isothermal = 89.20%

Concept:

COP of the system when two cycles with COP₁ and COP₂ are arranged in series is given by,

\(COP = \;\frac{{CO{P_1}\; \times \;CO{P_2}}}{{1\; + \;CO{P_1}\; + \;CO{P_2}}}\)

Calculation:

Given: 

COP₁ = 5 and COP₂ = 6

\(COP = \;\frac{{CO{P_1}\; \times \;CO{P_2}}}{{1\; + \;CO{P_1}\; + \;CO{P_2}}}\)

\(COP = \frac{{5\; \times \;6}}{{1\; + \;5\; + \;6}} = \frac{{30}}{{12}} = 2.50\)

Explanation:

\(1 - 2' - 3 - 4 - 5 - 6\)

Multi-stage compression in VCR

1 – 2 – 5 – 6 = Ideal VCR

Multi-stage compression with intercooling

(a)  Reduces compressor outlet temperature

(b)  Compression of refrigerant near-saturated vapor line

(c)  Reduce work input

Explanation:

Joule – Thomson coefficient:- When the gas in steady flow passes through a constriction, e.g. in an orifice or valve, it normally experiences a change in temperature. From the first law of thermodynamics, such a process is isenthalpic and one can usefully define a Joule – Thomson coefficient as

\(\mu = {\left( {\frac{{\partial T}}{{\partial P}}} \right)_H}\)

As a measure of the change in temperature which results from a drop in pressure across the construction.

• For an ideal gas, μ = 0, because ideal gases neither warm not cool upon being expanded at constant enthalpy.
• If μ is +ve, then the temperature will fall during throttling.
• If μ is -ve, then the temperature will rise during throttling.

For Perfect  or ideal gas μ = 0

Since \(\mu = {\left( {\frac{{\delta T}}{{\delta P}}} \right)_h} = 0\therefore \delta T = 0, \;{T_1} = {T_2}\)

Hence, During liquefication of perfect gas through expansion or throttling remains constant.

Concept:

COP of the system when two cycles with COP₁ and COP₂ are arranged in series is given by,

\(COP = \;\frac{{CO{P_1}\; \times \;CO{P_2}}}{{1\; + \;CO{P_1}\; + \;CO{P_2}}}\)

Calculation:

Given: 

COP₁ = 5 and COP₂ = 6

\(COP = \;\frac{{CO{P_1}\; \times \;CO{P_2}}}{{1\; + \;CO{P_1}\; + \;CO{P_2}}}\)

\(COP = \frac{{5\; \times \;6}}{{1\; + \;5\; + \;6}} = \frac{{30}}{{12}} = 2.50\)

Explanation:

Cascade Refrigeration System

Definition: A cascade refrigeration system is a specialized type of refrigeration system that uses two or more refrigeration cycles with different refrigerants to achieve very low temperatures. Each cycle operates at different temperature ranges and is connected in series, where the evaporator of one cycle serves as the condenser for the next cycle.

Working Principle: In a cascade refrigeration system, multiple refrigeration circuits are used in stages, each with its own refrigerant that is best suited for the specific temperature range it operates within. The first stage (high-temperature stage) uses a refrigerant with a relatively higher boiling point, which condenses at a temperature that serves as the evaporator temperature for the second stage (low-temperature stage). The second stage uses a refrigerant with a much lower boiling point, capable of achieving extremely low temperatures.

For example, in a two-stage cascade system, the high-temperature stage might use a refrigerant such as R-134a, while the low-temperature stage might use a refrigerant like R-23. The high-temperature stage absorbs heat from the environment and transfers it to the low-temperature stage, where the second refrigerant absorbs the heat and evaporates at a much lower temperature, providing the desired refrigeration effect.

Advantages:

• Ability to achieve extremely low temperatures that are not possible with a single refrigeration cycle.
• Enhanced efficiency and performance by using refrigerants that are optimized for specific temperature ranges.
• Flexibility in selecting refrigerants that are environmentally friendly and suitable for the desired temperature range.

Disadvantages:

• Increased complexity in design and operation due to multiple refrigeration circuits and components.
• Higher initial cost and maintenance requirements compared to single-stage systems.
• Requires precise control and coordination between the different stages to ensure optimal performance.

Applications: Cascade refrigeration systems are commonly used in applications requiring very low temperatures, such as in cryogenics, pharmaceutical industries, and scientific research laboratories.

Analysis of Other Options:

Option 2: A single refrigerant in both cycles

This option is incorrect because a cascade refrigeration system specifically utilizes multiple refrigerants with different boiling points to achieve the desired temperature ranges. Using a single refrigerant in both cycles would not allow the system to reach extremely low temperatures effectively.

Option 3: Only ammonia as a refrigerant

This option is incorrect because while ammonia is a common refrigerant used in various refrigeration systems, a cascade refrigeration system requires multiple refrigerants with different boiling points to operate efficiently. Relying solely on ammonia would not provide the necessary temperature differential between the stages.

Option 4: Only air as a working fluid

This option is incorrect because air is not used as a refrigerant in cascade refrigeration systems. Refrigeration systems typically use refrigerants that undergo phase changes (liquid to vapor and vice versa) to absorb and reject heat. Air does not have the necessary properties to function effectively as a refrigerant in this context.

Explanation:

\(1 - 2' - 3 - 4 - 5 - 6\)

Multi-stage compression in VCR

1 – 2 – 5 – 6 = Ideal VCR

Multi-stage compression with intercooling

(a)  Reduces compressor outlet temperature

(b)  Compression of refrigerant near-saturated vapor line

(c)  Reduce work input

Concept:

\({\rm{Work\;}} = \frac{{Nn}}{{n - 1}} \times R{T_1} \times {\left( {\frac{{{P_d}}}{{{P_s}}}} \right)^{\frac{{n - 1}}{{Nn}}}} - 1\)

Isothermal work \( = R{T_1}\;ln\;\left( {\frac{{{P_s}}}{{{P_1}}}} \right)\)

\({\eta _{isothermal}} = \frac{{isothermal\;work}}{{polytropic\;work}}\)

Calculation:

Given: P₁ = 90 kPa = P_s, P_d = 4000 kPa, n = 1.31, N = 4

Now,

\({\rm{Compressor\;work\;}} = \frac{{4\; \times \;1.31}}{{0.31}} \times 0.287 \times 300 \times \left[ {{{\left( {\frac{{4000}}{{90}}} \right)}^{\frac{{0.31}}{{4\; \times \;1.31}}}} - 1} \right]\)

∴ Compressor work = 366.253 kJ/kg

Now,

\({\rm{Isothermal\;work}} = 0.287 \times 300 \times ln\left( {\frac{{4000}}{{90}}} \right)\)

∴ Isothermal work = 326.684 kJ/kg

\(\therefore \;{\eta _{isothermal}}\; = \frac{{326.689}}{{366.253}}\;\)

∴ η_isothermal = 89.20%

Concept:

COP of the system when two cycles with COP₁ and COP₂ are arranged in series is given by,

\(COP = \;\frac{{CO{P_1}\; \times \;CO{P_2}}}{{1\; + \;CO{P_1}\; + \;CO{P_2}}}\)

Calculation:

Given: 

COP₁ = 5 and COP₂ = 6

\(COP = \;\frac{{CO{P_1}\; \times \;CO{P_2}}}{{1\; + \;CO{P_1}\; + \;CO{P_2}}}\)

\(COP = \frac{{5\; \times \;6}}{{1\; + \;5\; + \;6}} = \frac{{30}}{{12}} = 2.50\)

Explanation:

Joule – Thomson coefficient:- When the gas in steady flow passes through a constriction, e.g. in an orifice or valve, it normally experiences a change in temperature. From the first law of thermodynamics, such a process is isenthalpic and one can usefully define a Joule – Thomson coefficient as

\(\mu = {\left( {\frac{{\partial T}}{{\partial P}}} \right)_H}\)

As a measure of the change in temperature which results from a drop in pressure across the construction.

• For an ideal gas, μ = 0, because ideal gases neither warm not cool upon being expanded at constant enthalpy.
• If μ is +ve, then the temperature will fall during throttling.
• If μ is -ve, then the temperature will rise during throttling.

For Perfect  or ideal gas μ = 0

Since \(\mu = {\left( {\frac{{\delta T}}{{\delta P}}} \right)_h} = 0\therefore \delta T = 0, \;{T_1} = {T_2}\)

Hence, During liquefication of perfect gas through expansion or throttling remains constant.

Explanation:

Cascade Refrigeration System

Definition: A cascade refrigeration system is a specialized type of refrigeration system that uses two or more refrigeration cycles with different refrigerants to achieve very low temperatures. Each cycle operates at different temperature ranges and is connected in series, where the evaporator of one cycle serves as the condenser for the next cycle.

Working Principle: In a cascade refrigeration system, multiple refrigeration circuits are used in stages, each with its own refrigerant that is best suited for the specific temperature range it operates within. The first stage (high-temperature stage) uses a refrigerant with a relatively higher boiling point, which condenses at a temperature that serves as the evaporator temperature for the second stage (low-temperature stage). The second stage uses a refrigerant with a much lower boiling point, capable of achieving extremely low temperatures.

For example, in a two-stage cascade system, the high-temperature stage might use a refrigerant such as R-134a, while the low-temperature stage might use a refrigerant like R-23. The high-temperature stage absorbs heat from the environment and transfers it to the low-temperature stage, where the second refrigerant absorbs the heat and evaporates at a much lower temperature, providing the desired refrigeration effect.

Advantages:

• Ability to achieve extremely low temperatures that are not possible with a single refrigeration cycle.
• Enhanced efficiency and performance by using refrigerants that are optimized for specific temperature ranges.
• Flexibility in selecting refrigerants that are environmentally friendly and suitable for the desired temperature range.

Disadvantages:

• Increased complexity in design and operation due to multiple refrigeration circuits and components.
• Higher initial cost and maintenance requirements compared to single-stage systems.
• Requires precise control and coordination between the different stages to ensure optimal performance.

Applications: Cascade refrigeration systems are commonly used in applications requiring very low temperatures, such as in cryogenics, pharmaceutical industries, and scientific research laboratories.

Analysis of Other Options:

Option 2: A single refrigerant in both cycles

This option is incorrect because a cascade refrigeration system specifically utilizes multiple refrigerants with different boiling points to achieve the desired temperature ranges. Using a single refrigerant in both cycles would not allow the system to reach extremely low temperatures effectively.

Option 3: Only ammonia as a refrigerant

This option is incorrect because while ammonia is a common refrigerant used in various refrigeration systems, a cascade refrigeration system requires multiple refrigerants with different boiling points to operate efficiently. Relying solely on ammonia would not provide the necessary temperature differential between the stages.

Option 4: Only air as a working fluid

This option is incorrect because air is not used as a refrigerant in cascade refrigeration systems. Refrigeration systems typically use refrigerants that undergo phase changes (liquid to vapor and vice versa) to absorb and reject heat. Air does not have the necessary properties to function effectively as a refrigerant in this context.

Concept:

Cascade Refrigeration System:

• When the required lower temperature is very low the pressure ratio increases drastically, hence the volumetric efficiency becomes very low then cascade refrigeration system is used.
• It is used for storage of blood plasma.
• For manufacturing of dry ice (solid form of CO₂)
• For Liquification of petroleum gases used.

Calculation:

Given:

(COP)₁ = 2.3

(COP)₂ = 1.6

(COP)_overall = \(\frac{(COP)_1~\times ~(COP)_2}{1~+~(COP)_1~+~(COP)_2}\)

(COP)_overall = \(\frac{(2.3)~\times ~(1.6)}{1~+~(2.3)~+~(1.6)}\) = 0.75

Concept:

COP of the system when two cycles with COP₁ and COP₂ are arranged in series is given by,

\(COP = \;\frac{{CO{P_1}\; \times \;CO{P_2}}}{{1\; + \;CO{P_1}\; + \;CO{P_2}}}\)

Calculation:

Given, COP₁ = 5 and COP₂ = 6

\(COP = \frac{{5\; \times \;6}}{{1\; + \;5\; + \;6}} = \frac{{30}}{{12}} = 2.50\)

Concept:

The cascade refrigeration system is a freezing system employing two kinds of refrigerants having different boiling points, which run through their own independent freezing cycle and are connected by a heat exchanger. In cascade refrigeration system, the higher-temperature side uses a normally used refrigerant (R404A, ammonia, etc.), and the lower-temperature side uses R23, which is an HFC refrigerant

COP of such a system is given by

\(COP = \;\frac{{CO{P_1}\; \times \;CO{P_2}}}{{1 + \;CO{P_{1\;}} + \;CO{P_2}}}\)

Calculation:

Net effective COP:

\({\rm{COP}} = \frac{{3{\rm{\;}} \times 2.25}}{{1 + 3 + 2.25}} = 1.08\)