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A reversible thermodynamic cycle containing only three processes and producing work is to be constructed. The constraints are :
(i) there must be one isothermal process,
(ii) there must be one isentropic process,
(iii) the maximum and minimum cycle pressures and the clearance volume are fixed, and
(iv) polytropic processes are not allowed. Then the number of possible cycles are
(i) there must be one isothermal process,
(ii) there must be one isentropic process,
(iii) the maximum and minimum cycle pressures and the clearance volume are fixed, and
(iv) polytropic processes are not allowed. Then the number of possible cycles are
[2005]
- a)1
- b)2
- c)3
- d)4
Correct answer is option 'A'. Can you explain this answer?
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A reversible thermodynamic cycle containing only three processes and p...
Given information:
- The reversible thermodynamic cycle contains only three processes.
- The cycle must produce work.
- Constraints:
(i) There must be one isothermal process.
(ii) There must be one isentropic process.
(iii) The maximum and minimum cycle pressures and the clearance volume are fixed.
(iv) Polytropic processes are not allowed.
Solution:
To determine the number of possible cycles, let's consider the constraints and analyze the possible combinations.
1. Isothermal Process:
Since there must be one isothermal process in the cycle, we have the following options for the isothermal process:
- Isothermal Expansion: Occurs when the gas expands at constant temperature.
- Isothermal Compression: Occurs when the gas is compressed at constant temperature.
2. Isentropic Process:
Since there must be one isentropic process in the cycle, we have the following options for the isentropic process:
- Isentropic Expansion: Occurs when the gas expands with no heat transfer and no entropy change.
- Isentropic Compression: Occurs when the gas is compressed with no heat transfer and no entropy change.
3. Maximum and Minimum Cycle Pressures:
The maximum and minimum cycle pressures are fixed. Let's denote the maximum pressure as Pmax and the minimum pressure as Pmin.
4. Clearance Volume:
The clearance volume is fixed. Let's denote it as Vc.
Possible Combinations:
Based on the given constraints, we can have the following combinations:
1. Isothermal Expansion - Isentropic Compression - Isothermal Compression
2. Isothermal Compression - Isentropic Expansion - Isothermal Expansion
Explanation:
There are only two possible combinations that satisfy all the given constraints. These combinations involve an isothermal process, an isentropic process, and a combination of expansion and compression processes. Since the question asks for the number of possible cycles, the correct answer is option 'A', which is 1.
It is important to note that the specific details of the cycle and the specific values of the pressures and clearance volume are not provided in the question. Therefore, the analysis is based on the given constraints and the general understanding of thermodynamic cycles.
- The reversible thermodynamic cycle contains only three processes.
- The cycle must produce work.
- Constraints:
(i) There must be one isothermal process.
(ii) There must be one isentropic process.
(iii) The maximum and minimum cycle pressures and the clearance volume are fixed.
(iv) Polytropic processes are not allowed.
Solution:
To determine the number of possible cycles, let's consider the constraints and analyze the possible combinations.
1. Isothermal Process:
Since there must be one isothermal process in the cycle, we have the following options for the isothermal process:
- Isothermal Expansion: Occurs when the gas expands at constant temperature.
- Isothermal Compression: Occurs when the gas is compressed at constant temperature.
2. Isentropic Process:
Since there must be one isentropic process in the cycle, we have the following options for the isentropic process:
- Isentropic Expansion: Occurs when the gas expands with no heat transfer and no entropy change.
- Isentropic Compression: Occurs when the gas is compressed with no heat transfer and no entropy change.
3. Maximum and Minimum Cycle Pressures:
The maximum and minimum cycle pressures are fixed. Let's denote the maximum pressure as Pmax and the minimum pressure as Pmin.
4. Clearance Volume:
The clearance volume is fixed. Let's denote it as Vc.
Possible Combinations:
Based on the given constraints, we can have the following combinations:
1. Isothermal Expansion - Isentropic Compression - Isothermal Compression
2. Isothermal Compression - Isentropic Expansion - Isothermal Expansion
Explanation:
There are only two possible combinations that satisfy all the given constraints. These combinations involve an isothermal process, an isentropic process, and a combination of expansion and compression processes. Since the question asks for the number of possible cycles, the correct answer is option 'A', which is 1.
It is important to note that the specific details of the cycle and the specific values of the pressures and clearance volume are not provided in the question. Therefore, the analysis is based on the given constraints and the general understanding of thermodynamic cycles.
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A reversible thermodynamic cycle containing only three processes and producing work is to be constructed. The constraints are :(i) there must be one isothermal process,(ii) there must be one isentropic process,(iii) the maximum and minimum cycle pressures and the clearance volume are fixed, and(iv) polytropic processes are not allowed. Then the number of possible cycles are[2005]a)1b)2c)3d)4Correct answer is option 'A'. Can you explain this answer?
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