The air in a cylinder is at a pressure of 14.7 lb/in.^2 and occupies a volume of 175 in.^3 Find the pressure when it is compressed to 25.0 in^3.
To find the pressure when the air is compressed to a new volume, we can use Boyle's Law, which states that the product of the initial pressure and volume is equal to the product of the final pressure and volume.
The initial pressure (P1) is 14.7 lb/in^2, and the initial volume (V1) is 175 in^3.
The final volume (V2) is given as 25.0 in^3.
Using Boyle's Law, we can set up the equation:
P1 * V1 = P2 * V2
Substituting the given values into the equation:
14.7 lb/in^2 * 175 in^3 = P2 * 25.0 in^3
Now we can solve for P2 (the final pressure):
P2 = (14.7 lb/in^2 * 175 in^3) / 25.0 in^3
Calculating the numerator:
14.7 lb/in^2 * 175 in^3 = 2572.5 lb/in^2 * in^3
Now we can divide the numerator by the denominator to get the final pressure:
P2 = 2572.5 lb/in^2 * in^3 / 25.0 in^3
Simplifying the units:
P2 = 2572.5 lb/in
Therefore, the pressure when the air is compressed to 25.0 in^3 is 2572.5 lb/in^2.