One mole of an ideal gas does 3400 J of work on its surroundings as it expands isothermally to a final pressure of 1.00 atm and volume of 22.0 L.

Question

(a) Determine the initial volume in m^3.

i tried using the formula w=integral f/i pdv
3400J= -(1.00atm)(.022m^3Vf-Vi)
i eneded with 1.55 x10^5 but htis is not the right answer. HELP PLS!

Answer 1

Isothermal expansion
W = integral p dv
p = n R T/v, T constant so
W = n R T integral dv/v
W = n R T ln v from v1 to v2
W = n R T ln(v2/v1)
here
n = 1
R = R =.08206 L atm/mol degK or 8.31 J/mol deg K
Need T, use v2
T = p2 v2/nR = 1*22/1*.082
T = 268 deg K
now we want to use Joules and scientific notaton R
V2 = 22 L = 22* 10^-3 m^3
3400 = 1 * 8.31 * 268 ln (22*10^-3/v)
ln(.022/v)= 1.53
.022/v = 4.6
v = .00478 m^3 = 4.78 Liters