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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 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.
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.
Most Upvoted Answer
Let dw be the work done in a quasistatic reversible thermodynamic proc...
The statement that is correct is option 'B': dw is a perfect differential if the process is adiabatic.
Explanation:
To understand why this statement is correct, let's first understand what a perfect differential is. In thermodynamics, a perfect differential is a quantity that depends only on the initial and final states of a system and not on the path taken to reach those states. In other words, it is a quantity that can be integrated to give a unique value.
Now, let's consider the options given:
a) dw is a perfect differential if the process is isothermal.
This statement is not correct. In an isothermal process, the temperature remains constant. The work done in an isothermal process can be calculated using the equation: dw = PdV, where P is the pressure and dV is the change in volume. Since pressure and volume can vary continuously during an isothermal process, dw is not a perfect differential.
b) dw is a perfect differential if the process is adiabatic.
This statement is correct. In an adiabatic process, there is no heat exchange between the system and its surroundings. This means that any work done on or by the system is solely due to the change in its internal energy. In other words, the work done in an adiabatic process can be expressed as a function of the initial and final states of the system, making dw a perfect differential.
c) dw is always a perfect differential.
This statement is not correct. As mentioned earlier, dw is not a perfect differential in all processes. It depends on the conditions of the process, such as whether it is isothermal or adiabatic.
d) dw cannot be a perfect differential.
This statement is not correct. As we have seen, dw can be a perfect differential in certain processes, such as adiabatic processes.
In conclusion, the correct statement is option 'B': dw is a perfect differential if the process is adiabatic.
Explanation:
To understand why this statement is correct, let's first understand what a perfect differential is. In thermodynamics, a perfect differential is a quantity that depends only on the initial and final states of a system and not on the path taken to reach those states. In other words, it is a quantity that can be integrated to give a unique value.
Now, let's consider the options given:
a) dw is a perfect differential if the process is isothermal.
This statement is not correct. In an isothermal process, the temperature remains constant. The work done in an isothermal process can be calculated using the equation: dw = PdV, where P is the pressure and dV is the change in volume. Since pressure and volume can vary continuously during an isothermal process, dw is not a perfect differential.
b) dw is a perfect differential if the process is adiabatic.
This statement is correct. In an adiabatic process, there is no heat exchange between the system and its surroundings. This means that any work done on or by the system is solely due to the change in its internal energy. In other words, the work done in an adiabatic process can be expressed as a function of the initial and final states of the system, making dw a perfect differential.
c) dw is always a perfect differential.
This statement is not correct. As mentioned earlier, dw is not a perfect differential in all processes. It depends on the conditions of the process, such as whether it is isothermal or adiabatic.
d) dw cannot be a perfect differential.
This statement is not correct. As we have seen, dw can be a perfect differential in certain processes, such as adiabatic processes.
In conclusion, the correct statement 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 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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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 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? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE 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 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? covers all topics & solutions for GATE 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 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?.
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 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? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE 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 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? covers all topics & solutions for GATE 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 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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