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A system at a given state undergoes change through the following expansion processes to reach the same final volume
1. Isothermal
2. Isobaric
3. Adiabatic ( γ = 1.4)
4. Polytropic(n =1.3)
The correct ascending order of the work output in these four processes is
- a)3, 4, 1, 2
- b)1, 4, 3, 2
- c)4, 1, 3, 2
- d)4, 1, 2, 3
Correct answer is option 'A'. Can you explain this answer?
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A system at a given state undergoes change through the following expan...
Explanation:
The work output in each of the four expansion processes can be calculated using the following formulas:
1. Isothermal: W = nRT ln(Vf/Vi)
2. Isobaric: W = P(Vf - Vi)
3. Adiabatic: W = (PfVf - PiVi)/(γ-1)
4. Polytropic: W = (PfVf - PiVi)/(n-1)
where n is the number of moles of gas, R is the universal gas constant, T is the temperature, P is the pressure, V is the volume, γ is the ratio of specific heats, and n is the polytropic index.
Ascending order of work output:
1. Isothermal: In an isothermal process, the temperature remains constant, and the work output is given by W = nRT ln(Vf/Vi). As ln(Vf/Vi) is always less than or equal to 0, the work output in an isothermal process is always negative. Therefore, the work output in an isothermal process is the lowest among the four processes.
2. Isobaric: In an isobaric process, the pressure remains constant, and the work output is given by W = P(Vf - Vi). As the pressure remains constant, the work output in an isobaric process is greater than that in an isothermal process.
3. Adiabatic: In an adiabatic process, no heat is exchanged between the system and the surroundings, and the work output is given by W = (PfVf - PiVi)/(γ-1). As γ > 1, the work output in an adiabatic process is greater than that in an isobaric process.
4. Polytropic: In a polytropic process, the pressure and volume are related by the equation PV^n = constant, where n is the polytropic index. The work output in a polytropic process is given by W = (PfVf - PiVi)/(n-1). As n > γ, the work output in a polytropic process is the greatest among the four processes.
Therefore, the correct ascending order of the work output in these four processes is 3, 4, 1, 2.
The work output in each of the four expansion processes can be calculated using the following formulas:
1. Isothermal: W = nRT ln(Vf/Vi)
2. Isobaric: W = P(Vf - Vi)
3. Adiabatic: W = (PfVf - PiVi)/(γ-1)
4. Polytropic: W = (PfVf - PiVi)/(n-1)
where n is the number of moles of gas, R is the universal gas constant, T is the temperature, P is the pressure, V is the volume, γ is the ratio of specific heats, and n is the polytropic index.
Ascending order of work output:
1. Isothermal: In an isothermal process, the temperature remains constant, and the work output is given by W = nRT ln(Vf/Vi). As ln(Vf/Vi) is always less than or equal to 0, the work output in an isothermal process is always negative. Therefore, the work output in an isothermal process is the lowest among the four processes.
2. Isobaric: In an isobaric process, the pressure remains constant, and the work output is given by W = P(Vf - Vi). As the pressure remains constant, the work output in an isobaric process is greater than that in an isothermal process.
3. Adiabatic: In an adiabatic process, no heat is exchanged between the system and the surroundings, and the work output is given by W = (PfVf - PiVi)/(γ-1). As γ > 1, the work output in an adiabatic process is greater than that in an isobaric process.
4. Polytropic: In a polytropic process, the pressure and volume are related by the equation PV^n = constant, where n is the polytropic index. The work output in a polytropic process is given by W = (PfVf - PiVi)/(n-1). As n > γ, the work output in a polytropic process is the greatest among the four processes.
Therefore, the correct ascending order of the work output in these four processes is 3, 4, 1, 2.
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A system at a given state undergoes change through the following expansion processes to reach the same final volume1. Isothermal2. Isobaric3. Adiabatic ( = 1.4)4. Polytropic(n =1.3)The correct ascending order of the work output in these four processes isa)3, 4, 1, 2b)1, 4, 3, 2c)4, 1, 3, 2d)4, 1, 2, 3Correct answer is option 'A'. Can you explain this answer?
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