Finding new Pressure in cylinder when compressed

[yopy]

http://img15.imageshack.us/img15/9746/21478397.png

I know how to setup the entire problem i just don't know how to calculate the new pressure after the piston is compressed.

 

[rock.freak667]

At constant temperature P is proportional to 1/V , or PV=constant.

 

[Blueshift5]

To calculate the new pressure in the cylinder after compression, we can use the ideal gas law, which states that the pressure (P) and volume (V) of a gas are inversely proportional when the temperature (T) is constant. This can be expressed as P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.

In this case, we can use the given information to solve for the final pressure (P2). We know that the initial pressure (P1) is 101.3 kPa (standard atmospheric pressure) and the initial volume (V1) is 1000 cm^3. We also know that the final volume (V2) is 500 cm^3, as the piston has been compressed by half.

Plugging these values into the ideal gas law equation, we get:

P1V1 = P2V2
(101.3 kPa)(1000 cm^3) = P2(500 cm^3)

Solving for P2, we get:

P2 = (101.3 kPa)(1000 cm^3) / (500 cm^3)
P2 = 202.6 kPa

Therefore, the new pressure in the cylinder after compression is 202.6 kPa. It is important to note that this calculation assumes that the temperature remains constant during compression, which may not always be the case in real-world scenarios. Other factors such as heat transfer and energy loss may also affect the final pressure. Further analysis and experimentation may be needed to accurately determine the new pressure in these situations.