Heat and the first Law of thermodynamics

I have the following question and I'm still sortof confused as to how the change in internal energy is zero.

Question: A sample of $1.5\,\mathrm{mol}$ of diatomic gas is at an initial pressure of $3\,\mathrm{atm}$ and at a volume of $2.2\,\mathrm{L}$. the gas expands isothermally until the volume doubles. what is the change in internal energy of the gas and how much work does it do during the expansion.

we know Workdone on = - Workdone by, thus workdone by the gas \begin{align} W &= nRT\ln2\\ \Delta E &= C_v\Delta T + nRT\ln2 \end{align} because the process is isothermal: $\Delta T=0$ thus $$\Delta E=nRT\ln2$$.

However my professor stated in class that \begin{align}\Delta E &= C_v\Delta T \\ &= 0 \end{align}

I'm still confused as to how $\Delta E = 0$ and not $\Delta E = nRT\ln2$

I'd really appreciate it if someone could enlighten me on this.

Thanks!