Question

which is a correct way of stating boyles law?
select the correct answer below:
$p = k \times \frac{1}{v}$, where $k$ is a constant.
$pv = k$, where $k$ is a constant.
$p_1v_1 = p_2v_2$, where the indices 1 and 2 corresponds to different states of the same gas sample.
all of the above

Explanation:

Step1: Analyze \(P = k\times\frac{1}{V}\)

Boyle's law states that for a given mass of an ideal gas at a constant temperature, pressure \(P\) is inversely proportional to volume \(V\). So \(P=\frac{k}{V}\) (where \(k\) is a constant) is a valid form.

Step2: Analyze \(PV = k\)

From \(P=\frac{k}{V}\), cross - multiplying gives \(PV = k\) (where \(k\) is a constant), which is also a valid form of Boyle's law.

Step3: Analyze \(P_1V_1=P_2V_2\)

If we consider two different states (state 1 and state 2) of the same gas sample (same \(k\) since mass and temperature are constant), from \(PV = k\), we have \(P_1V_1=P_2V_2\).

Since all the given equations are valid representations of Boyle's law, the answer is all of the above.

Answer:

all of the above