Question

According to Boyle's law, if a gas has a volume of 150 cm³ and exerts a pressure of (6 X 10^4 N/m^2), what is the pressure if the volume is reduced to 80 cm³?

A. (3.75 X 10^4 N/m^2)
B. (9 X 10^4 N/m^2)
C. (1.125 X 10^5 N/m^2)
D. (2.4 X 10^5 N/m^2)

Answer 1

According to Boyle's law, the pressure and volume of a gas are inversely proportional at a constant temperature. The final pressure can be calculated using the formula P₁V₁ = P₂V₂. In this case, the final pressure (P₂) is 1.125 X 10^5 N/m².

Step-by-step explanation:

According to Boyle's law, the pressure and volume of a gas are inversely proportional at a constant temperature. Boyle's law can be expressed as: P₁V₁ = P₂V₂. Given that the initial volume (V₁) is 150 cm³ and the initial pressure (P₁) is 6 X 10^4 N/m², we can solve for the final pressure (P₂) when the volume (V₂) is reduced to 80 cm³.

Using the formula, P₁V₁ = P₂V₂, we can plug in the known values: (6 X 10^4 N/m²)(150 cm³) = P₂(80 cm³). We can then solve for P₂ by dividing both sides of the equation by 80 cm³ and multiplying both sides by (6 X 10^4 N/m²): P₂ = (6 X 10^4 N/m²)(150 cm³) / 80 cm³.

Calculating this expression gives us a final pressure (P₂) of 1.125 X 10^5 N/m². Therefore, the correct answer is C. (1.125 X 10^5 N/m²).