A student conducts a series of measurements on a sample of gas in a container. Match each … — ACT

A student conducts a series of measurements on a sample of gas in a container. Match each experimental variable relationship on the left with its correct proportional trend on the right.

The relationship between gas pressure ( $P$ ) and gas volume ( $V$ ) at a constant temperature ( $P = \frac{k}{V}$ )Inverse proportionality
The relationship between gas volume ( $V$ ) and absolute temperature ( $T$ ) at a constant pressure ( $V = kT$ )Direct proportionality
The relationship between gas pressure ( $P$ ) and volume ( $V$ ) when pressure is controlled to remain constant ( $P = c$ )No proportionality

Answer

The relationship between gas pressure and gas volume at a constant temperature matches with inverse proportionality. The relationship between gas volume and absolute temperature at a constant pressure matches with direct proportionality. The relationship between gas pressure and volume when pressure is controlled to remain constant matches with no proportionality.

The correct pairings align the inverse relationship of pressure and volume to inverse proportionality, the direct relationship of volume and temperature to direct proportionality, and the constant pressure relationship to no proportionality.

Step-by-Step Solution

Examine the relationship between gas pressure and gas volume at constant temperature.

The formula

P = \frac{k}{V}

shows that pressure is inversely proportional to volume.

As volume increases, pressure decreases by the same factor.

Examine the relationship between gas volume and absolute temperature at constant pressure.

The formula

V = kT

shows that volume is directly proportional to absolute temperature.

As absolute temperature increases, volume increases by the same factor.

Examine the relationship between gas pressure and volume when pressure is kept constant.

The formula

P = c

shows that pressure does not change regardless of volume.

Since pressure remains constant, there is no proportional change.

Key Concept

Identifying direct and inverse proportional relationships from physical equations.

Estimated Time:1m 0s

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