According to the ideal gas laws, which relationship is true for Boyle's Law?

Boyle's Law describes the inverse relationship between pressure and volume for a given quantity of gas at constant temperature. According to this law, when the volume of a gas decreases, the pressure increases, assuming the temperature is held constant. This is mathematically represented as ( P \propto \frac{1}{V} ), indicating that pressure is inversely proportional to volume.

This relationship holds true under ideal conditions where no other variables (like temperature or the amount of gas) are changing. Thus, for Boyle's Law, if you were to halve the volume of a gas, the pressure would double, affirming this inverse proportionality.

In contrast, the other relationships described do not reflect the nature of Boyle's Law:

• If pressure were directly proportional to temperature, that would signify a different law (Charles's Law), which holds temperature constant in relation to volume.

• A direct proportionality between pressure and volume contradicts the observations described by Boyle's Law, as it suggests that an increase in volume would result in increased pressure, which is opposite to the correct relationship.

• Pressure being proportional to the square of the volume (i.e., ( P \propto V^2 )) does not hold true for any gas behavior