## Expansion of a gas at constant temperature and pressure

1. The problem statement, all variables and given/known data

A gas expands in volume from 26.7mL to 89.3mL at constant temperature. Calculate the work done (in joule) if the gas expands:
i) against a vacuum
ii) against constant pressure of 1.5atm
iii) against a constant pressure of 2.8

2. Relevant equations

w= -PdV

gas expands at constant temperature= isothemic expansion

3. The attempt at a solution

ii) 1atm= 1.013x10^5 Pa

P= 1.5x 1.013x10^5 = 151950 Pa

I converted ml to m^3 (am i supposed to do this?)

26.7/ 1x10^6 = 2.67x10^-5 m^3

8.93/ 1x10^6 = 8.93x10^-5 m^3

w= -PdV

w= - (151950)x (8.93x10^-5 -2.67x10^-5)

w= -9.512 J

iii) I did the same working for this part as above

P= 2.8 x 1.013x10^5

P= 283640 Pa

w= - (283640) x (8.93x10^-5 -2.67x10^-5)

w= -17.756 J

am I doing this correct? or do I use the equation ln V2/V1 P ?
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 i) That's free expansion; It's as if the gas is 'doing work' by pushing a massless piston in space since there's no opposing force as the gas expands. ii & iii) It's isothermal expansion, so P varies as the volume changes. The equation W = -P ∆V doesn't work anymore and W = -∫ P dv, is used instead. Also, yeah, it's better to convert ml to cubic meters since it's simpler to keep everything in the MKS system of units.

 Tags constant pressure, expansion of a gas