One mole of an ideal gas does 3200J of work on itssurroundings as it expands iso

Question

One mole of an ideal gas does 3200J of work on itssurroundings as it expands isothermally to a final pressure of 1.00atm and volume of 28.0L Determine the initial volume. I tried using W= -P(Vf-Vi), but pressure isn't constant, so Icouldn't get the right answer. Please help. Thanks. One mole of an ideal gas does 3200J of work on itssurroundings as it expands isothermally to a final pressure of 1.00atm and volume of 28.0L Determine the initial volume. I tried using W= -P(Vf-Vi), but pressure isn't constant, so Icouldn't get the right answer. Please help. Thanks.

Explanation / Answer

w = integral [-p*dV] p = nRT/V w = -integral [nRT *dV/V] = -nRT* ln(V2/V1) nRT = P1*V1 = 1 atm*28 L = 28 L-atm w = -28L-atm *ln(V2/V1) V1 = V2/exp(w/-28L-atm)      = 28 L *exp(3200 J / [28 L-atm *101325Pa/atm *(1m3/1000 L)])      = 9.06 L

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