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Question
$\mathrm{5~mol}$ of a gas is confined in a piston (volume $\mathrm{100~cm^3}$) at $\mathrm{400~K}$. $\mathrm{10~kJ}$ of heat energy is supplied, causing a reversible and isothermal expansion of the gas. Calculate the volume of the expanded, heated, gas. You may use the equation below (assume ideal gas behaviour).

$$W = -nRT(\ln V_2-\ln V_1)$$

I substituted the values (after converting to SI units) into the equation and attempted to rearrange to find $V_2$, but work was unknown. I tried to use the enthalpy value (10 kJ) given but I was unsure of what to do with it.

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I dont understand where you are getting stuck up since everything is already given to you and you just have to substitute stuff using:

$\Delta U= W+Q$, the basic conservation equation.

$Q$ is the heat supplied. Think about the change in internal energy ($U$) during an isothermal process.

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