Question

Which statement correctly relates the variables described in Boyle’s law?

Answer 1

The correct statement is: "For a gas, pressure multiplied by volume is constant at constant temperature."

Boyle's Law describes the relationship between the pressure and volume of a gas at constant temperature. The correct statement is: "For a gas, pressure multiplied by volume is constant at constant temperature."

Boyle's Law is mathematically expressed as
`\(PV = \text{constant}\)`, where
`\(P\)` is the pressure, and
`\(V\)` is the volume of the gas. This means that when the pressure of a gas increases, its volume decreases, and vice versa, as long as the temperature remains constant. In other words, the product of pressure and volume is constant for a given amount of gas at constant temperature.

To understand this concept, consider a fixed amount of gas confined in a container. If the volume of the container is reduced (compression), the gas particles collide more frequently with the container walls, resulting in an increase in pressure. Conversely, if the volume is increased (expansion), the gas particles collide less frequently with the container walls, leading to a decrease in pressure.

Mathematically, Boyle's Law can be expressed as:

`\[ P_1V_1 = P_2V_2 \]`

where
`\(P_1\)` and
`\(V_1\)` are the initial pressure and volume, and
`\(P_2\)` and
`\(V_2\)` are the final pressure and volume.

The correct statement emphasizes that the product of pressure and volume,
`\(PV\)`, remains constant when temperature is held constant. This is a fundamental principle that helps explain the behavior of gases under different conditions.

Answer 2

Step 1 - Understanding Boyle's Law

Boyle's Law is an empirical observation concerning the behavior of gases. When the temperature is kept constant, Boyle observed that a linear relationship arised between pressure and volume.

Boyle observed they were inversely proportional, i.e., raising the pressure would decrease the volume and vice-versa. We can state it mathematically as:

`P_1V_1=P_2V_2`

Which means that the multiplication between pressure and volume is a constant value:

`PV=k`

Step 2 - Finding the correct statement

We can start by looking for the statements which contain "constant temperature". In the absence of this condition, Boyle's Law is inconsistent. We are left thus with itens a and b.

Since Boyle's Law involves multiplication, not the quotient between the variables pressure and volume, the correc statement in item b (the 2nd one from top to bottom).