To determine the new volume of the gas when the pressure increases to 400 atm while the temperature remains constant, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional when temperature is held constant.
According to Boyle's Law:
P₁V₁ = P₂V₂
Where: P₁ = Initial pressure (200 atm) V₁ = Initial volume (10 L) P₂ = Final pressure (400 atm) V₂ = Final volume (unknown)
Let's plug in the given values into the equation:
200 atm * 10 L = 400 atm * V₂
Simplifying the equation, we have:
2000 atm·L = 400 atm * V₂
Now, let's solve for V₂:
V₂ = (2000 atm·L) / 400 atm V₂ = 5 L
Therefore, the new volume of the gas, when the pressure increases to 400 atm at constant temperature, would be 5 liters.