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?
Answer Details
The pressure of the gas will decrease to \(frac{3}{2}\) P when its volume is increased to 2V at constant temperature.
This can be explained using Boyle's law, which states that the pressure of a gas is inversely proportional to its volume, when temperature is held constant. In other words, as the volume of a gas increases, its pressure will decrease proportionally and vice versa.
Given that the initial volume and pressure of the gas are V and 3.P, respectively, we can write:
P1V1 = P2V2
where P1 is the initial pressure, V1 is the initial volume, P2 is the final pressure, and V2 is the final volume.
Substituting the given values, we get:
(3.P) V = P2 (2V)
Simplifying this equation, we get:
P2 = (3.P) V / (2V)
P2 = \(frac{3}{2}\) P
Therefore, the pressure of the gas will decrease to \(frac{3}{2}\) P when its volume is increased to 2V at constant temperature.