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Derive an expression for maximum work in isothermal reversible expansion of 'n'moles of an ideal gas?
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Derive an expression for maximum work in isothermal reversible expansi...
Maximum Work in Isothermal Reversible Expansion of Ideal Gas
An isothermal reversible expansion is a process in which an ideal gas expands while its temperature remains constant. The expansion is reversible, which means that the gas can be compressed back to its original state without any loss of energy. The maximum work that can be obtained from this process can be derived using the following equation:
W = -nRT ln(Vf/Vi)
where:
- W is the work done by the gas
- n is the number of moles of the gas
- R is the gas constant
- T is the temperature of the gas
- Vf is the final volume of the gas
- Vi is the initial volume of the gas
Explanation
The equation for the maximum work done by an ideal gas during an isothermal reversible expansion can be derived using the following steps:
- Assume that the gas is expanding slowly and reversibly, and that the temperature remains constant throughout the process.
- Use the first law of thermodynamics to calculate the change in internal energy of the gas:
- dU = dQ - dW
- Since the process is isothermal, dU = 0
- Therefore, dQ = dW
- Use the ideal gas law to express dQ in terms of changes in pressure and volume:
- dQ = nCv dT
- Since the temperature is constant, dT = 0
- Therefore, dQ = 0
- Using the ideal gas law, PV = nRT, we can express dQ in terms of changes in pressure and volume:
- dQ = Cv dT = Cv (PfVf - PiVi)
- Substitute dQ = dW into the equation:
- Cv (PfVf - PiVi) = dW
- Since the process is reversible, the work done by the gas is maximum:
- Therefore, dW = -PdV
- Integrate the equation for dW:
- W = -∫PiPf PdV
- Since the process is isothermal, P = nRT/V
- Therefore, W = -∫ViVf nRT/V dV = -nRT ln(Vf/Vi)
Therefore, the maximum work that can be obtained from an isothermal reversible expansion of an ideal gas is given by the equation:
W = -nRT ln(Vf/Vi)
Community Answer
Derive an expression for maximum work in isothermal reversible expansi...
W.d.is nrT ln(v/V)
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Derive an expression for maximum work in isothermal reversible expansion of 'n'moles of an ideal gas?
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Derive an expression for maximum work in isothermal reversible expansion of 'n'moles of an ideal gas? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Derive an expression for maximum work in isothermal reversible expansion of 'n'moles of an ideal gas? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Derive an expression for maximum work in isothermal reversible expansion of 'n'moles of an ideal gas?.
Derive an expression for maximum work in isothermal reversible expansion of 'n'moles of an ideal gas? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Derive an expression for maximum work in isothermal reversible expansion of 'n'moles of an ideal gas? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Derive an expression for maximum work in isothermal reversible expansion of 'n'moles of an ideal gas?.
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