Question

a group of students trap gas in an expandable container and measures 3 variables using sensors. they record the results as variables a, b, and c below.
what are variables b and c most likely?
a pressure and volume
b volume and number of particles
c temperature and pressure
d number of particles and pressure

Explanation:

According to Boyle's law, \(P \propto\frac{1}{V}\) (at constant temperature and amount of gas). Here, variable \(A\) is constant (assume it as temperature, as in Boyle's law - temperature is constant for the relationship between pressure and volume). When variable \(B\) (assume volume) increases, variable \(C\) (assume pressure) decreases. For example, when \(B = 2.0\), \(C=20.0\); when \(B = 4.0\), \(C = 10.0\); when \(B=6.0\), \(C = 6.7\) (approx \(\frac{20}{3}\)), when \(B = 8.0\), \(C=5.0\); when \(B = 10.0\), \(C = 4.0\). The product \(B\times C\) is approximately constant (\(2\times20 = 40\), \(4\times10=40\), \(6\times6.7\approx40\), \(8\times5 = 40\), \(10\times4=40\)), which follows \(PV = k\) (constant, where \(P\) is pressure and \(V\) is volume)

Answer:

A. Pressure and volume