To analyze the relationships between volume, pressure, and temperature of an enclosed gas, we can refer to the ideal gas law, which can be summarized as:
\[ PV = nRT \]
Where:
- \( P \) is the pressure,
- \( V \) is the volume,
- \( n \) is the number of moles of gas,
- \( R \) is the universal gas constant,
- \( T \) is the temperature in Kelvin.
From this equation, we can derive the relationships:
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Volume (V) and Temperature (T): At constant pressure, if the temperature increases, the volume also increases. Therefore, volume and temperature are directly proportional.
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Pressure (P) and Volume (V): At constant temperature, if the pressure increases, the volume decreases. Therefore, pressure and volume are inversely proportional.
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Pressure (P) and Temperature (T): At constant volume, if the temperature increases, the pressure also increases. Therefore, pressure and temperature are directly proportional.
Given these relationships, we have:
- Volume and Temperature: Directly Proportional
- Pressure and Volume: Inversely Proportional
- Pressure and Temperature: Directly Proportional
Using this analysis, the correct option is:
Quantities Relationship: volume and temperature directly proportional; pressure and volume inversely proportional; pressure and temperature directly proportional.
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