Question

if the gas in the above system has a volume of v at a pressure of p, what is the volume of the same gas at a pressure of 4p? your answer should be given as a decimal number rounded to the nearest hundredth. give your answer in terms of \v\ ex. 1v, 2v, 0.5v etc.

Explanation:

Step1: Apply Boyle's Law

Boyle's Law states \(P_1V_1 = P_2V_2\). Here, \(P_1 = P\), \(V_1=V\), \(P_2 = 4P\).
Substitute into the formula: \(P\times V=4P\times V_2\).

Step2: Solve for \(V_2\)

Divide both sides of the equation \(PV = 4PV_2\) by \(4P\).
\(V_2=\frac{PV}{4P}\). The \(P\) terms cancel out (\(P
eq0\)), so \(V_2=\frac{V}{4}= 0.25V\).

Answer:

\(0.25V\)