Work Done when a Gas is Compressed

In order to calculate the work done when a gas is compressed, we need to use the formula:

Work Done (W) = -PΔV

Where:
- W represents the work done
- P is the average pressure applied to the gas
- ΔV is the change in volume of the gas

Given data:
- Average pressure (P) = 0.50 Atm
- Initial volume (Vi) = 400 cm^3
- Final volume (Vf) = 200 cm^3

Step 1: Calculate the change in volume (ΔV)
The change in volume can be calculated by subtracting the final volume from the initial volume:

ΔV = Vf - Vi
= 200 cm^3 - 400 cm^3
= -200 cm^3

Note: The negative sign indicates a decrease in volume.

Step 2: Calculate the work done (W)
Now, we can substitute the values into the formula:

W = -PΔV
= -(0.50 Atm)(-200 cm^3)
= 100 Atm·cm^3

Step 3: Convert the units (Optional)
If required, we can convert the units of work done to another system. For example, 1 Atm·cm^3 is equivalent to 101.3 Joules (J).

W = 100 Atm·cm^3 × 101.3 J/Atm·cm^3
= 10130 J

Therefore, the work done when the gas is compressed by an average pressure of 0.50 Atm, resulting in a volume decrease from 400 cm^3 to 200 cm^3, is 10130 Joules (J).

Summary:
- The work done when a gas is compressed is given by the formula W = -PΔV.
- The change in volume (ΔV) is calculated by subtracting the final volume from the initial volume.
- The negative sign in front of the formula indicates a decrease in volume.
- The units of work done can be converted if necessary, such as from Atm·cm^3 to Joules (J).

100j