To find the new volume of the gas when the pressure is increased from 2 atmospheres to 6 atmospheres while keeping the temperature constant, we can use Boyle's law.
Boyle's law states that the pressure and volume of a gas are inversely proportional when temperature is held constant. Mathematically, it can be expressed as:
P₁V₁ = P₂V₂
Where: P₁ = Initial pressure V₁ = Initial volume P₂ = Final pressure V₂ = Final volume
Given: P₁ = 2 atmospheres V₁ = 8 liters P₂ = 6 atmospheres (new pressure)
Let's substitute these values into the equation and solve for V₂:
P₁V₁ = P₂V₂
(2)(8) = (6)(V₂)
16 = 6V₂
Divide both sides of the equation by 6:
16/6 = V₂
Simplifying the division:
V₂ ≈ 2.67 liters
Therefore, the new volume of the gas, when the pressure is increased to 6 atmospheres while keeping the temperature constant, will be approximately 2.67 liters.