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An ideal gas is compressed to half its initial volume by means of several processes. Which of the processes results in the maximum work done on the gas?
- a)Isobaric
- b)Isochoric
- c)Isothermal
- d)Adiabatic
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
An ideal gas is compressed to half its initial volume by means of sev...
Polytropic Process is represented by
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PVn = C
- n = 0 ⇒ P = C ⇒ Constant Pressure Process (Isobaric Process)
- n = 1 ⇒ PV = C ⇒ Constant Temperature Process (Isothermal process)
- n = γ ⇒ PVγ = C ⇒ Adiabatic Process
- n = ∞ ⇒ V = C ⇒ Constant Volume Process (Isochoric process)
Area under P-V diagrams represents the work done.
For compression between two volumes, we can see that area is maximum for the adiabatic process.
So work done on the gas will be maximum for the adiabatic process.
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An ideal gas is compressed to half its initial volume by means of sev...
Understanding Work Done on an Ideal Gas
When compressing an ideal gas to half its initial volume, the work done on the gas varies depending on the process used. Let's analyze why the adiabatic process results in the maximum work done.
Work Done in Different Processes
- Isobaric Process:
- The pressure remains constant while the volume decreases.
- Work done is given by W = P(ΔV). Since pressure is constant, this results in moderate work done.
- Isochoric Process:
- The volume remains constant, meaning no work is done (W = 0).
- This process does not contribute to work done on the gas.
- Isothermal Process:
- The temperature remains constant, requiring heat to be absorbed as work is done on the gas.
- While the work done can be significant, it is limited by the heat exchange.
- Adiabatic Process:
- No heat exchange occurs with the surroundings.
- The work done is maximized because all energy goes into doing work on the gas, raising its internal energy and thus its pressure.
Why Adiabatic Process Maximizes Work
- In an adiabatic compression, the lack of heat exchange means that all the energy input is converted to work.
- The temperature of the gas increases, leading to a steeper pressure-volume curve.
- This results in a higher pressure at a smaller volume, allowing for greater work done on the gas compared to the other processes.
Conclusion
In summary, the adiabatic process results in the maximum work done on an ideal gas when compressed to half its initial volume because it utilizes all the input energy for work, without any loss to heat.
When compressing an ideal gas to half its initial volume, the work done on the gas varies depending on the process used. Let's analyze why the adiabatic process results in the maximum work done.
Work Done in Different Processes
- Isobaric Process:
- The pressure remains constant while the volume decreases.
- Work done is given by W = P(ΔV). Since pressure is constant, this results in moderate work done.
- Isochoric Process:
- The volume remains constant, meaning no work is done (W = 0).
- This process does not contribute to work done on the gas.
- Isothermal Process:
- The temperature remains constant, requiring heat to be absorbed as work is done on the gas.
- While the work done can be significant, it is limited by the heat exchange.
- Adiabatic Process:
- No heat exchange occurs with the surroundings.
- The work done is maximized because all energy goes into doing work on the gas, raising its internal energy and thus its pressure.
Why Adiabatic Process Maximizes Work
- In an adiabatic compression, the lack of heat exchange means that all the energy input is converted to work.
- The temperature of the gas increases, leading to a steeper pressure-volume curve.
- This results in a higher pressure at a smaller volume, allowing for greater work done on the gas compared to the other processes.
Conclusion
In summary, the adiabatic process results in the maximum work done on an ideal gas when compressed to half its initial volume because it utilizes all the input energy for work, without any loss to heat.
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An ideal gas is compressed to half its initial volume by means of several processes. Which of the processes results in the maximum work done on the gas?a)Isobaricb)Isochoricc)Isothermald)AdiabaticCorrect answer is option 'D'. Can you explain this answer?
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