Suppose that subsequent to this heating, 1.10 104 J of thermal energy is removed

Question

Suppose that subsequent to this heating, 1.10 104 J of thermal energy is removed from the gas isothermally. Find the final volume in terms of the initial volume of the example, V0? (Hint: Follow the same steps as in the example, but in reverse. Use the values calculated in the solution portion. Also note that the initial volume in this exercise is 1.25 V0.)

Work of environment= 2968.029252
number of moles= 5.30
Temperature= 25 degrees celcius

I use this equation: Work of environment= nrt ln vfinal/vinitial
When I solve I keep getting vfinal= 0.44 X Vinital
I do not know what I am doing wrong?
Please Help?
Thanks

Explanation / Answer

The amount of energy removed Q = 1.10*10^4 J

The number of moles n = 5.3

the temperature T = 25 + 273 = 298 K

Since the gas expands isothermally so change in internal energy is zero

then W = Q = nRTln(Vf/Vi)

then   ln(Vf/Vi) = W/nRT

                        = 1.10*10^4 / (5.3)(8.31)(298)

                         = 0.838

therefore Vf/Vi = e^0.838

                        = 2.3V0

when W = 2968.029252

then Vf/Vi = e^ (2968.029252)/(5.3)(8.31)(298)

           Vf     = 1.25 V0

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