Question

calculate the work associated with a system when its volume is expanded from 51.2 l to 90 l against a constant pressure of 1 bar. express your final answer in j.

Explanation:

Step1: Identify the formula for work

The formula for work done in a pressure - volume process is $w=-P\Delta V$.

Step2: Calculate the change in volume

$\Delta V = V_{final}-V_{initial}=90\ L - 51.2\ L= 38.8\ L$.

Step3: Convert pressure and volume units

We know that $1\ bar = 10^{5}\ Pa$ and $1\ L=10^{- 3}\ m^{3}$. So, $P = 1\ bar=10^{5}\ Pa$ and $\Delta V=38.8\ L = 38.8\times10^{-3}\ m^{3}$.

Step4: Calculate the work

$w=-P\Delta V=-10^{5}\ Pa\times38.8\times 10^{-3}\ m^{3}=- 3880\ J$. The negative sign indicates that the system is doing work on the surroundings. The magnitude of the work is $3880\ J$.

Answer:

$3880$