Answer
$V_2 = 0.226 m^3$
Work Step by Step
To find the volume in state 2, we should use the equation
$W = nRT ln (\frac{V_2}{V_1})$
From the answer in (d), $W = 700J$
From the question , $V_1 = 0.200 m^3$
and $T = 350 K $
$n = 2.00 mol$
$R = 8.314 J/k.mol $
Rearrange the equation to solve for $V_2$ and substitute all the values into the equation.
$\frac{W}{nRT} = ln (\frac{V_2}{V_1})$
$e^\frac{W}{nRT} = \frac{V_2}{V_1}$
$V_2 = (V_1) e^\frac{W}{nRT}$
$V_2 = (0.200 m^3) e^\frac{700J}{(2.00 mol)(8.314 J/k.mol )(350 K)}$
$V_2 = (0.200 m^3) e^{0.12}$
$V_2 = (0.200 m^3) 1.13$
$V_2 = 0.226 m^3$
