The initial volume and pressure of a given mass of gas is V and 3.P. What is its pressure if its volume is increased to  2V at constant temperature?

Analyze the question

A fixed mass of gas at constant temperature changes volume from V to 2V. We are asked for the new pressure. The initial pressure is written as "3.P", which means 3P (the "." is a typo-style separator, and the options confirm this).

Concept: Boyle's Law

At constant temperature, the pressure of a fixed mass of gas is inversely proportional to its volume:

P₁V₁ = P₂V₂

Solution

• P₁ = 3P
• V₁ = V
• V₂ = 2V
• P₂ = ?

(3P)(V) = P₂(2V)

P₂ = 3PV / 2V = (3/2)P

Doubling the volume should halve the pressure, and half of 3P is 1.5P, which matches our result.

Answer: Option C, (3/2)P.

Tip: For Boyle's Law, if the volume is multiplied by a factor, the pressure is divided by the same factor. Here the volume is ×2, so the pressure is ÷2: 3P ÷ 2 = 3P/2. Also, watch out for option B (2P), which comes from wrongly treating the initial pressure as P instead of 3P.