Question

Which of the following is NOT a correct equation for adiabatic process?

• A. \(PV^{\gamma }=constant\)
• B. \(TV^{\gamma -1}=constant\)
• C. \(P^{1-\gamma }T^{\gamma }=constant\)
• D. \(P^{\gamma -1}T^{\gamma -1}=constant\)

Hint:

Start from the adiabatic relation for pressure and volume and use the gas law to convert to other variable pairs.

Answer 1

The Correct Option is D

Step 1: Recall the standard forms
The three standard adiabatic forms are $PV^{\gamma}$, $TV^{\gamma-1}$ and $P^{1-\gamma}T^{\gamma}$, each equal to a constant.

Step 2: Compare the options
Options (A), (B) and (C) match these forms exactly.

Step 3: Why option D fails
The pressure exponent has the wrong sign. With $P^{\gamma-1}$ and $T^{\gamma-1}$ both positive, the relation would need $PT$ to stay constant, which is not true in an adiabatic change.

Final Answer:
Only option (D) is not one of the standard adiabatic relations. \[ \boxed{\text{(D) }P^{\gamma -1}T^{\gamma -1}=\text{constant}} \]