A cylinder of gas is compressed by a piston from an intial volume of 125 litres to a final volume of 90 litres.The compression occurs at constant pressure and work done on the gas by the piston is 10^4J.What is the gas pressure during compression

To find the gas pressure during compression, we can use the formula for work done on a gas:

Work = Pressure * Change in Volume

We are given that the initial volume (V1) of the cylinder is 125 liters and the final volume (V2) is 90 liters. The work done (W) on the gas by the piston is 10^4 J.

Let's calculate the change in volume:

Change in Volume = V2 - V1
Change in Volume = 90 L - 125 L
Change in Volume = -35 L (note that the change is negative because the volume is decreasing)

Now we can rearrange the formula to solve for pressure:

Pressure = Work / Change in Volume

Substituting the given values:

Pressure = 10^4 J / -35 L

To find the gas pressure, we need to convert liters to cubic meters, as the SI unit for volume is cubic meters. We know that 1 liter is equal to 0.001 cubic meters.

Pressure = 10^4 J / (-35 L * 0.001 m^3/L)

Now, simplify:

Pressure = 10^4 J / (-0.035 m^3)

Finally, calculate the pressure:

Pressure ≈ -2.857 x 10^5 Pa

Therefore, the gas pressure during compression is approximately -2.857 x 10^5 Pa. Note that the pressure is negative because the cylinder is being compressed.