Answer:
[tex]W=640Pam^3=640J[/tex]
Explanation:
To calculate the work, given a change in volume we use the following formula:
[tex]W=p\Delta V=p(v_{f}-v_{i})[/tex]
Where [tex]W[/tex] is work, [tex]p[/tex] is pressure, [tex]v_{f}[/tex] is the final volume, and [tex]v_{i}[/tex] is the initial volume.
In this case:
[tex]p=200kPa=200x10^3Pa[/tex]
[tex]v_{f}=3.4l[/tex]
[tex]v_{i}=0.2l[/tex]
We need to convert liters to [tex]m^3[/tex] (to get joule units in the work ) Since [tex]1l=0.001m^3[/tex]
[tex]v_{f}=3.4l=0.0034m^3[/tex]
[tex]v_{i}=0.2l=0.0002m^3[/tex]
Thus, thw work is:
[tex]W=200x10^3Pa(0.0034m^3-0.0002m^3)[/tex]
[tex]W=200x10^3Pa(0.0032m^3)[/tex]
[tex]W=640Pam^3=640J[/tex]
the value of work in the expansion is [tex]640J[/tex]
This question involves the concepts of work done by the piston and the pressure-volume-work equation.
The value of work done will be "640 J".
The pressure-volume-work equation is given as follows:
[tex]W=P\Delta V[/tex]
where,
W = Work done by the piston = ?
P = External pressure = 200 KPa = 200000 Pa
ΔV = Change in volume = 3.4 L - 0.2 L = 3.2 L = 0.0032 m³
Therefore,
[tex]W=(200000\ Pa)(0.0032\ m^3)[/tex]
W = 640 J
Learn more about work done by piston here:
https://brainly.com/question/3406116?referrer=searchResults
The attached picture shows pressure-volume-work equation.
