Question

which law can be derived from the ideal gas law? select the correct answer below: boyles law charless law amontonss law all of the above

Explanation:

Step1: Ideal gas law formula

The ideal gas law is \(PV = nRT\).

Step2: Derive Boyle's law

If \(n\) (moles of gas) and \(T\) (temperature) are constant (\(nRT=\text{constant}\)), then \(PV=\text{constant}\) or \(P_1V_1 = P_2V_2\) (Boyle's law: \(P\propto\frac{1}{V}\) at constant \(n\) and \(T\)).

Step3: Derive Charles's law

If \(n\) and \(P\) are constant (\(\frac{nR}{P}=\text{constant}\)), then \(\frac{V}{T}=\text{constant}\) or \(\frac{V_1}{T_1}=\frac{V_2}{T_2}\) (Charles's law: \(V\propto T\) at constant \(n\) and \(P\)).

Step4: Derive Amontons's law

If \(n\) and \(V\) are constant (\(\frac{nR}{V}=\text{constant}\)), then \(\frac{P}{T}=\text{constant}\) or \(\frac{P_1}{T_1}=\frac{P_2}{T_2}\) (Amontons's law: \(P\propto T\) at constant \(n\) and \(V\)).

So all of the given laws (Boyle's, Charles's, Amontons's) can be derived from the ideal gas law.

Answer:

all of the above