Calculate and show the solution of certain gas expands in volume from 2.0 L to 6.0 L at constant temperature. Calculate the work done by the gas if it expands
a. against a vacuum and
b. against a constant pressure of 1.2 atm
a. against a vacuum and
b. against a constant pressure of 1.2 atm
Answers & Comments
Answer:
To calculate the work done by the gas as it expands, we can use the equation:
Work = -PΔV
where P is the pressure and ΔV is the change in volume.
a. Against a Vacuum:
In this case, the gas expands against a vacuum, which means there is no external pressure acting on the gas. Therefore, the work done is zero.
Work = -PΔV = -0 x (6.0 L - 2.0 L) = 0
b. Against a Constant Pressure of 1.2 atm:
In this case, the gas expands against a constant pressure of 1.2 atm. The change in volume (ΔV) is calculated as the final volume minus the initial volume.
ΔV = 6.0 L - 2.0 L = 4.0 L
The work done is then calculated using the formula:
Work = -PΔV
Work = -(1.2 atm) x (4.0 L) = -4.8 atm⋅L
So, the work done by the gas as it expands against a constant pressure of 1.2 atm is -4.8 atm⋅L. The negative sign indicates that work is done on the gas, as it is expanding.