In adiabatic process

Options

A. `PV^(gamma)`=constant
B. `TV^(gamma-1)`=constant
C. `P^(gamma)V=`constant
D. Both (1) & (2)

Answer

To solve the question regarding the adiabatic process, we need to analyze the properties and equations that define it. Here is a step-by-step solution:

### Step 1: Understand the Adiabatic Process
An adiabatic process is one in which no heat is exchanged with the surroundings. This means that any change in the internal energy of the system is due to work done on or by the system.

### Step 2: Identify the Key Equations
In thermodynamics, there are three important equations that describe an adiabatic process for an ideal gas:
1. \( PV^\gamma = \text{constant} \)
2. \( PV^{\gamma - 1} = \text{constant} \)
3. \( P^{1 - \gamma} V^\gamma = \text{constant} \)

Where:
- \( P \) is the pressure,
- \( V \) is the volume,
- \( \gamma \) (gamma) is the heat capacity ratio (Cp/Cv).

### Step 3: Analyze the Given Options
The question provides options in the form of equations. We need to check which of these options correspond to the equations stated above.

1. **Option 1**: \( PV^\gamma = \text{constant} \) (This matches the first equation)
2. **Option 2**: \( PV^{\gamma - 1} = \text{constant} \) (This matches the second equation)
3. **Option 3**: \( P^{1 - \gamma} V^\gamma = \text{constant} \) (This matches the third equation)

### Step 4: Determine the Correct Options
From the analysis:
- Option 1 is correct as it matches the first equation.
- Option 2 is correct as it matches the second equation.
- Option 3 is also correct as it matches the third equation.

### Conclusion
Since options 1, 2, and 3 are all correct, the final answer would indicate that options 1 and 2 are correct, and option 3 is also valid. Therefore, the correct conclusion is that all three equations are valid representations of an adiabatic process.