At a constant temperature, the pressure, P, and volume, V, of a trapped gas have the relationship P equals the quotient of k divided by V , where k is some positive constant. What occurs if the volume is compressed such that V → 0+?


The pressure increases without bound.

The pressure decreases without bound.

The pressure approaches zero.

The pressure remains constant.

P = k/V

as v->0, P->∞

To determine what happens if the volume is compressed such that V → 0+, we need to understand the relationship between pressure (P) and volume (V) as described in the question.

According to the given relationship, P equals k/V, where k is a positive constant. This relationship implies that as the volume decreases (denoted by V → 0+), the pressure increases.

In simple terms, as the gas is compressed to smaller volumes, the particles of the gas are forced closer together, leading to more frequent collisions with the container walls. These frequent collisions result in an increase in pressure.

Therefore, the correct answer is: The pressure increases without bound.