A sample of oxygen gas expands in volume from 1.6 L to 5.4 L at constant temperature. What is the work done in joules if the gas expands against a constant pressure of 0.80 atm?

Dec 24, 2016

The work is $- 307.95 \text{ Joules} .$

Explanation:

Work involved in a isotermic expansion is given by:

$W = - p \cdot \Delta V$

Then, if a ${V}_{1}$ volume of gas expands to ${V}_{2}$ under a pressure $p$, the work done is:

$W = - p \cdot \left({V}_{2} - {V}_{1}\right)$.

We have:

${V}_{1} = 1.6 \textcolor{w h i t e}{\text{."} L = 1.6 cdot 10^{- 3} color(white) {".}} {m}^{3}$

${V}_{2} = 5.4 \textcolor{w h i t e}{\text{."} L = 5.4 cdot 10^{-3} color(white) {".}} {m}^{3}$

$p = 0.80 \textcolor{w h i t e}{\text{."} atm = 0.80 cdot 101,300 color(white) {"."} Pa = 81,040 color(white) {".}} P a$

Then:

$W = - p \cdot \Delta V = - p \cdot \left({V}_{2} - {V}_{1}\right) =$

$= - 81 , 040 \textcolor{w h i t e}{\text{."} Pa cdot (0.0054 - 0.0016) color(white) {"."} m^3 = - 307.95 color(white) {".}} J$.