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?

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Answer 1 · 2016-12-24T19:20:09

The work is #- 307.95 " Joules".#

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 (V_2 - V_1)#.

We have:

#V_1 = 1.6 color(white) {"."} L = 1.6 cdot 10^{- 3} color(white) {"."} m^3#

#V_2 = 5.4 color(white) {"."} L = 5.4 cdot 10^{-3} color(white) {"."} m^3#

#p = 0.80 color(white) {"."} atm = 0.80 cdot 101,300 color(white) {"."} Pa = 81,040 color(white) {"."} Pa#

Then:

#W = - p cdot Delta V = - p cdot (V_2 - V_1) =#

#= - 81,040 color(white) {"."} Pa cdot (0.0054 - 0.0016) color(white) {"."} m^3 = - 307.95 color(white) {"."} J#.