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Let dw be the work done in a quasistatic reversible thermodynamic process.
Which of the following statements about dw is correct?
Which of the following statements about dw is correct?
- a)dw is a perfect differential if the process is isothermal.
- b)dw is a perfect differential if the process is adiabatic
- c)dw is always a perfect differential.
- d)dw cannot be a perfect differential.
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Let dw be the work done in a quasistatic reversible thermodynamic proc...
The first law of thermodynamics can be given dQ = dU + dW
here dQ and dW both are path function and dU is state function.
For making dW a perfect differential, we take dQ = 0 So dU + dW = 0 dW = –dU and dQ = 0 occur in adiabatic process, so, dW0 is a perfect differential if the process is adiabatic.
here dQ and dW both are path function and dU is state function.
For making dW a perfect differential, we take dQ = 0 So dU + dW = 0 dW = –dU and dQ = 0 occur in adiabatic process, so, dW0 is a perfect differential if the process is adiabatic.
Most Upvoted Answer
Let dw be the work done in a quasistatic reversible thermodynamic proc...
The first law of thermodynamics can be given dQ = dU + dW
here dQ and dW both are path function and dU is state function.
For making dW a perfect differential, we take dQ = 0 So dU + dW = 0 dW = –dU and dQ = 0 occur in adiabatic process, so, dW0 is a perfect differential if the process is adiabatic.
here dQ and dW both are path function and dU is state function.
For making dW a perfect differential, we take dQ = 0 So dU + dW = 0 dW = –dU and dQ = 0 occur in adiabatic process, so, dW0 is a perfect differential if the process is adiabatic.
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Let dw be the work done in a quasistatic reversible thermodynamic proc...
Explanation:
In thermodynamics, a perfect differential is a property that is exact and independent of the path taken during a process. If a differential is not perfect, it is referred to as an inexact differential.
To determine whether dw is a perfect differential, we need to consider the conditions under which it occurs in various thermodynamic processes.
a) dw is a perfect differential if the process is isothermal:
In an isothermal process, the temperature of the system remains constant. During such a process, the work done on or by the system can be expressed as:
dw = -PdV
where P is the pressure and dV is the change in volume.
Since the pressure and volume are both state functions, dw is a perfect differential in an isothermal process.
b) dw is a perfect differential if the process is adiabatic:
In an adiabatic process, there is no heat transfer between the system and its surroundings. The work done on or by the system can be expressed as:
dw = -PdV + TdS
where S is the entropy and T is the temperature.
In an adiabatic process, the change in entropy (dS) is zero. Therefore, the second term in the expression for dw becomes zero, and we are left with:
dw = -PdV
Similar to the isothermal case, since the pressure and volume are state functions, dw is a perfect differential in an adiabatic process.
c) dw is always a perfect differential:
This statement is incorrect. As seen from the explanations above, dw is a perfect differential only in isothermal and adiabatic processes. In other thermodynamic processes, such as isobaric or isochoric processes, dw is not a perfect differential.
d) dw cannot be a perfect differential:
This statement is also incorrect. As explained earlier, dw is a perfect differential in both isothermal and adiabatic processes.
Therefore, the correct answer is option 'b': dw is a perfect differential if the process is adiabatic.
In thermodynamics, a perfect differential is a property that is exact and independent of the path taken during a process. If a differential is not perfect, it is referred to as an inexact differential.
To determine whether dw is a perfect differential, we need to consider the conditions under which it occurs in various thermodynamic processes.
a) dw is a perfect differential if the process is isothermal:
In an isothermal process, the temperature of the system remains constant. During such a process, the work done on or by the system can be expressed as:
dw = -PdV
where P is the pressure and dV is the change in volume.
Since the pressure and volume are both state functions, dw is a perfect differential in an isothermal process.
b) dw is a perfect differential if the process is adiabatic:
In an adiabatic process, there is no heat transfer between the system and its surroundings. The work done on or by the system can be expressed as:
dw = -PdV + TdS
where S is the entropy and T is the temperature.
In an adiabatic process, the change in entropy (dS) is zero. Therefore, the second term in the expression for dw becomes zero, and we are left with:
dw = -PdV
Similar to the isothermal case, since the pressure and volume are state functions, dw is a perfect differential in an adiabatic process.
c) dw is always a perfect differential:
This statement is incorrect. As seen from the explanations above, dw is a perfect differential only in isothermal and adiabatic processes. In other thermodynamic processes, such as isobaric or isochoric processes, dw is not a perfect differential.
d) dw cannot be a perfect differential:
This statement is also incorrect. As explained earlier, dw is a perfect differential in both isothermal and adiabatic processes.
Therefore, the correct answer is option 'b': dw is a perfect differential if the process is adiabatic.
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Let dw be the work done in a quasistatic reversible thermodynamic process.Which of the following statements about dw is correct?a)dw is a perfect differential if the process is isothermal.b)dw is a perfect differential if the process is adiabaticc)dw is always a perfect differential.d)dw cannot be a perfect differential.Correct answer is option 'B'. Can you explain this answer?
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Let dw be the work done in a quasistatic reversible thermodynamic process.Which of the following statements about dw is correct?a)dw is a perfect differential if the process is isothermal.b)dw is a perfect differential if the process is adiabaticc)dw is always a perfect differential.d)dw cannot be a perfect differential.Correct answer is option 'B'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about Let dw be the work done in a quasistatic reversible thermodynamic process.Which of the following statements about dw is correct?a)dw is a perfect differential if the process is isothermal.b)dw is a perfect differential if the process is adiabaticc)dw is always a perfect differential.d)dw cannot be a perfect differential.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let dw be the work done in a quasistatic reversible thermodynamic process.Which of the following statements about dw is correct?a)dw is a perfect differential if the process is isothermal.b)dw is a perfect differential if the process is adiabaticc)dw is always a perfect differential.d)dw cannot be a perfect differential.Correct answer is option 'B'. Can you explain this answer?.
Let dw be the work done in a quasistatic reversible thermodynamic process.Which of the following statements about dw is correct?a)dw is a perfect differential if the process is isothermal.b)dw is a perfect differential if the process is adiabaticc)dw is always a perfect differential.d)dw cannot be a perfect differential.Correct answer is option 'B'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about Let dw be the work done in a quasistatic reversible thermodynamic process.Which of the following statements about dw is correct?a)dw is a perfect differential if the process is isothermal.b)dw is a perfect differential if the process is adiabaticc)dw is always a perfect differential.d)dw cannot be a perfect differential.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let dw be the work done in a quasistatic reversible thermodynamic process.Which of the following statements about dw is correct?a)dw is a perfect differential if the process is isothermal.b)dw is a perfect differential if the process is adiabaticc)dw is always a perfect differential.d)dw cannot be a perfect differential.Correct answer is option 'B'. Can you explain this answer?.
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