The ideal gas equation for an adiabatic process is

Options

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

Answer

To solve the question regarding the ideal gas equation for an adiabatic process, we need to understand the relationship between pressure (P), volume (V), and temperature (T) in such processes.

### Step-by-Step Solution:

1. **Understanding Adiabatic Processes**:
- An adiabatic process is one in which no heat is exchanged with the surroundings. This means that all the work done on or by the system results in a change in internal energy.

2. **Ideal Gas Law**:
- The ideal gas law is given by the equation \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles of gas, \( R \) is the universal gas constant, and \( T \) is temperature.

3. **Adiabatic Condition**:
- For an ideal gas undergoing an adiabatic process, the relationship between pressure and volume can be expressed as:
\[ PV^{\gamma} = \text{constant} \]
- Here, \( \gamma \) (gamma) is the ratio of specific heats, defined as \( \gamma = \frac{C_p}{C_v} \), where \( C_p \) is the specific heat at constant pressure and \( C_v \) is the specific heat at constant volume.

4. **Conclusion**:
- Therefore, the ideal gas equation for an adiabatic process is:
\[ PV^{\gamma} = \text{constant} \]

### Final Answer:
The ideal gas equation for an adiabatic process is \( PV^{\gamma} = \text{constant} \).

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