The volume of a system is changed from 17.0 L to 32.0 L under a pressure of 1.23 atm. Calculate the work of the system?
Question
The volume of a system is changed from 17.0 L to 32.0 L under a pressure of 1.23 atm. Calculate the work of the system?
Solution
To calculate the work done by the system, we can use the formula for work done during an isobaric process (a process at constant pressure):
W = PΔV
where: W is the work done, P is the pressure, and ΔV is the change in volume.
First, we need to calculate the change in volume (ΔV). This is the final volume (Vf) minus the initial volume (Vi):
ΔV = Vf - Vi ΔV = 32.0 L - 17.0 L ΔV = 15.0 L
Next, we need to convert the pressure from atm to the SI unit of pressure, which is pascals (Pa). 1 atm is approximately equal to 101325 Pa:
P = 1.23 atm * 101325 Pa/atm P = 124,749.75 Pa
Now we can calculate the work done:
W = PΔV W = 124,749.75 Pa * 15.0 L
However, we need to convert the volume from liters to cubic meters (m^3) because 1 m^3 = 1000 L:
W = 124,749.75 Pa * 15.0 L * 1 m^3/1000 L W = 124,749.75 Pa * 0.015 m^3 W = 1,871.24625 J
So, the work done by the system is approximately 1,871.25 Joules.
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