According to Boyle's law, the pressure p of a compressed gas is inversely proportional to the volume, v. If a pressure of 20 pounds per square inch exists when the volume of the gas is 500 cubic inches, what is the pressure when the gas is compressed to 400 cubic inches?

thanks but how did you get 1000 by dividing k by 500?

thank you so much! i really appreciate it!

The pressure P of a compressed gas is inversely proportional to the volume V. If there is a pressure of 25 pounds per square inch when the volume of gas is 400 cubic inches, write the equation that can be used to find the pressure when the gas is compressed to 200 cubic inches?

W varies inversely as the square of t. If W = 12 when t = 2, what equation can be used to solve for t when W = 27.

2+2

To solve this problem using Boyle's law, we need to understand the relationship between pressure and volume. Boyle's law states that when the temperature and the number of gas particles remain constant, the pressure of a gas is inversely proportional to its volume. Mathematically, this can be expressed as:

p₁v₁ = p₂v₂

Where p₁ and v₁ are the initial pressure and volume, respectively, and p₂ and v₂ are the final pressure and volume, respectively.

In this problem, we are given the initial pressure, p₁ = 20 pounds per square inch, and the initial volume, v₁ = 500 cubic inches. We need to find the final pressure, p₂, when the gas is compressed to a volume of v₂ = 400 cubic inches.

Using Boyle's law, we can set up the equation as follows:

20 * 500 = p₂ * 400

To solve for p₂, we can rearrange the equation:

p₂ = (20 * 500) / 400

p₂ = 25 pounds per square inch (Answer)

Therefore, the pressure when the gas is compressed to 400 cubic inches is 25 pounds per square inch.

I had 20 = k/500

now multiply both sides by 500
20(500) = (k/500)(500

10000=k

the 500's canceled on the right side

PROOF: 2/LOG A BASE 9 - 1/ LOG A BASE 5 = 3/ LOG A BASE 3

P = k/V

when P=20, V=500, so
20 = k/500
k = 10000
then P = 10000/V

if V - 400,
P = 10000/400 = 25

don't forget the units