Which of the following relations does not give the equation of an adiabatic process, where tems have their usual meaning ?

Options

A. `P^(gamma)T^(1-gamma)` = constant
B. `P^(1-gamma)T^(gamma)` = constant
C. `PV^(gamma)`= constant
D. `TV^(gamma-1)` = constant

Answer

To solve the problem of identifying which relation does not represent an adiabatic process, we need to analyze the equations related to adiabatic processes in thermodynamics.

### Step-by-Step Solution:

1. **Understanding Adiabatic Processes**:
An adiabatic process is one in which no heat is exchanged with the surroundings. The key equations for an adiabatic process involving an ideal gas are:
- \( PV^\gamma = \text{constant} \)
- \( TV^{\gamma - 1} = \text{constant} \)
- \( PT^\frac{\gamma}{\gamma - 1} = \text{constant} \)
where \( \gamma \) (gamma) is the heat capacity ratio \( C_p/C_v \).

2. **Identifying the Options**:
We need to evaluate the given options to see which one does not conform to the adiabatic relations mentioned above. Let's denote the options as:
- Option A: \( P^\gamma T^{-\gamma} = \text{constant} \)
- Option B: \( P^{1 - \gamma} T^\gamma = \text{constant} \)
- Option C: \( PV^\gamma = \text{constant} \)
- Option D: \( TV^{\gamma - 1} = \text{constant} \)

3. **Analyzing Each Option**:
- **Option A**: \( P^\gamma T^{-\gamma} = \text{constant} \) can be rewritten as \( P^\gamma = \text{constant} \cdot T^\gamma \). This does not match any standard adiabatic equation.
- **Option B**: \( P^{1 - \gamma} T^\gamma = \text{constant} \) can be derived from the adiabatic relation \( PV^\gamma = \text{constant} \) and is valid.
- **Option C**: \( PV^\gamma = \text{constant} \) is the standard equation for an adiabatic process.
- **Option D**: \( TV^{\gamma - 1} = \text{constant} \) is also a valid equation for an adiabatic process.

4. **Conclusion**:
Since Option A does not conform to the standard equations of adiabatic processes, it is the correct answer to the question.

### Final Answer:
**Option A: \( P^\gamma T^{-\gamma} = \text{constant} \)** does not give the equation of an adiabatic process.