Answer
$\Delta S=3.59\frac{J}{K}$
Work Step by Step
We know that:
$dQ=dE_{int}=\frac{3}{2}nRdT$
Now,
$\Delta S=\int \frac{dQ}{T}$
Therefore;
$\Delta S=\int _{T_i}^{T_f}\frac{\frac{3}{2}nRdT}{T} $
$\implies \Delta S=\frac{3}{2}nR\ln(\frac{T_f}{T_i})$
We plug in the known values to obtain:
$\Delta S=\frac{3 }{2}(1.00)(8.31)\ln(\frac{400}{300})=3.59\frac{J}{K}$
