Which table correctly shows the relationships between volume, pressure, and temperature of an enclosed gas?

Answer 1

The relationships between volume, pressure, and temperature of an enclosed gas are described by the ideal gas law, expressed mathematically as:

\[ PV = nRT \]

Where:

• \( P \) = Pressure
• \( V \) = Volume
• \( n \) = Number of moles of the gas
• \( R \) = Universal gas constant
• \( T \) = Temperature in Kelvin

From this equation, we can derive several important relationships:

1. Boyle’s Law: \( P \propto \frac{1}{V} \) (at constant temperature, as volume increases, pressure decreases, and vice versa.)

2. Charles’s Law: \( V \propto T \) (at constant pressure, as temperature increases, volume increases, and vice versa.)

3. Gay-Lussac's Law: \( P \propto T \) (at constant volume, as temperature increases, pressure increases, and vice versa.)

To create a table that illustrates these relationships, it should contain the following scenarios:

| Condition | Pressure (P) | Volume (V) | Temperature (T) | Relationship Type | |------------------|------------------|------------------|-------------------|--------------------| | Constant Temp | Increases | Decreases | Constant (T) | Boyle’s Law | | Constant Pressure | Increases | Increases | Increases (T) | Charles’s Law | | Constant Volume | Increases | Constant (V) | Increases (T) | Gay-Lussac's Law |

This table effectively highlights how changing one variable affects the others when the other factors are held constant.

Answer 2

Quantities Relationship
volume and temperature directly proportional
pressure and volume directly proportional
pressure and temperature inversely proportionalQuantities Relationship volume and temperature directly proportional pressure and volume directly proportional pressure and temperature inversely proportional

Quantities Relationship
volume and temperature directly proportional
pressure and volume inversely proportional
pressure and temperature directly proportionalQuantities Relationship volume and temperature directly proportional pressure and volume inversely proportional pressure and temperature directly proportional

Quantities Relationship
volume and temperature inversely proportional
pressure and volume inversely proportional
pressure and temperature directly proportionalQuantities Relationship volume and temperature inversely proportional pressure and volume inversely proportional pressure and temperature directly proportional

Quantities Relationship
volume and temperature inversely proportional
pressure and volume directly proportional
pressure and temperature directly proportional

Answer 3

Let's analyze the relationships provided in your options based on the principles of gas laws:

1. Volume and Temperature: Directly proportional (as per Charles's Law).
2. Pressure and Volume: Inversely proportional (as per Boyle's Law).
3. Pressure and Temperature: Directly proportional (as per Gay-Lussac's Law).

Based on this analysis, here’s the correct classification of relationships:

• Volume and Temperature: Directly Proportional
• Pressure and Volume: Inversely Proportional
• Pressure and Temperature: Directly Proportional

Therefore, the correct choice for the relationships is:

Quantities | Relationship -----------------------------|-------------------- Volume and Temperature | Directly Proportional Pressure and Volume | Inversely Proportional Pressure and Temperature | Directly Proportional

This means that the second option you provided correctly states the relationships.

Correct answer:

• Quantities Relationship
  • Volume and temperature: directly proportional
  • Pressure and volume: inversely proportional
  • Pressure and temperature: directly proportional