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Gas equation PV = nRT is obeyed by...

Gas equation `PV = nRT` is obeyed by

A

only isothermal process

B

only adiabatic process

C

both A and B

D

None of these

Text Solution

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The correct Answer is:
To determine which processes obey the gas equation \( PV = nRT \), we will analyze the two types of processes mentioned: isothermal and adiabatic. ### Step-by-Step Solution: 1. **Understanding the Ideal Gas Law**: The ideal gas equation is given by \( PV = nRT \), where: - \( P \) = Pressure of the gas - \( V \) = Volume of the gas - \( n \) = Number of moles of the gas - \( R \) = Universal gas constant - \( T \) = Temperature of the gas in Kelvin 2. **Isothermal Process**: - In an isothermal process, the temperature (\( T \)) remains constant. - Since \( T \) is constant, the equation \( PV = nRT \) can still be applied, and the relationship between pressure and volume can be described as \( PV = \text{constant} \). - Therefore, the isothermal process **obeys the ideal gas law**. 3. **Adiabatic Process**: - In an adiabatic process, there is no heat exchange with the surroundings (\( Q = 0 \)). - While the temperature may change during an adiabatic process, the ideal gas law can still be applied. The relationship between pressure, volume, and temperature can be described using the adiabatic equation, which is derived from the ideal gas law. - Thus, the adiabatic process **also obeys the ideal gas law**. 4. **Conclusion**: - Since both isothermal and adiabatic processes obey the ideal gas law, the correct answer to the question is that the gas equation \( PV = nRT \) is obeyed by **both a and b**. ### Final Answer: The correct option is **both a and b**.
To determine which processes obey the gas equation \( PV = nRT \), we will analyze the two types of processes mentioned: isothermal and adiabatic. ### Step-by-Step Solution: 1. **Understanding the Ideal Gas Law**: The ideal gas equation is given by \( PV = nRT \), where: - \( P \) = Pressure of the gas - \( V \) = Volume of the gas ...
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