Thermodynamic Analysis of an Iso-Energetic Process
Question:
An iso-energetic process in a system must also be one in which:
- dq = 0
- dQ = dW
- dw = 0
- None of these
Answer:
The correct answer is: None of these
First Law of Thermodynamics:
dU = dq + dw
dU = dq + dw
Iso-energetic Process Definition:
In an iso-energetic process, the internal energy remains constant. That means:
dU = 0 ⇒ dq + dw = 0 ⇒ dq = -dw
In an iso-energetic process, the internal energy remains constant. That means:
dU = 0 ⇒ dq + dw = 0 ⇒ dq = -dw
Now let’s evaluate the options:
- Option a: dq = 0 — If there’s no heat transfer, then from
dq = -dwit followsdw = 0. But this is not a requirement for all iso-energetic processes. This condition is too restrictive. - Option b: dQ = dW — The actual relationship is
dq = -dw, not equal. Incorrect expression of the first law. - Option c: dw = 0 — Similarly, if
dw = 0thendq = 0, but this is not a requirement either. Work and heat can both be non-zero but opposite.
Conclusion:
In an iso-energetic process, there is no change in internal energy, but that does not mean that heat transfer or work must individually be zero or equal. It only requires that their sum is zero. Therefore, none of the listed conditions must be true.
In an iso-energetic process, there is no change in internal energy, but that does not mean that heat transfer or work must individually be zero or equal. It only requires that their sum is zero. Therefore, none of the listed conditions must be true.
✅ Final Answer:
None of these