At a pressure of 105 5 Nm−2 − 2 , a gas has a volume of 20m3 3 . Calculate the volume at 4 x 105 5 Nm−2 − 2 at constant temperature.

At a pressure of 105 ${}^5$Nm−2 ${}^{-2}$, a gas has a volume of 20m3 ${}^3$. Calculate the volume at 4 x 105 ${}^5$Nm−2 ${}^{-2}$ at constant temperature.

Answer Details

In order to solve this problem, we can apply **Boyle's Law**, which states that the **pressure** and **volume** of a gas are inversely proportional at a constant temperature. Mathematically, this is expressed as:

P₁V₁ = P₂V₂

Where:

• P₁ is the initial pressure: 105 Nm^-2
• V₁ is the initial volume: 20 m³
• P₂ is the final pressure: 4 x 105 Nm^-2
• V₂ is the final volume, which we need to find

Rearranging the formula to solve for V₂:

V₂ = (P₁V₁) / P₂

Substituting the given values:

V₂ = (105 Nm^-2 x 20 m³) / (4 x 105 Nm^-2)

By calculating:

V₂ = (2100 m³) / 4 x 105

V₂ = 5 m³

Therefore, at a pressure of 4 x 105 Nm^-2, the volume of the gas is 5 m³.