$I=I_0 \sin \omega t=I_0 \sin \left(\frac{\pi}{T} t\right)$

$Q =\int \limits_0^{ T } Idt \Rightarrow Q = I _0 \int\limits_0^{ T } \sin \left(\frac{\pi}{ T } t \right) d t$

$=\frac{-I_0}{\pi T}\left[\cos \left(\frac{\pi}{T} t \right)\right]_0=\frac{2 TI _0}{\pi}$

$\Rightarrow \quad I _0= Q \pi / 2 T$

$\text { Heat }=\int_0^T I^2 R d t=\int_0^T I_0^2 \sin ^2\left(\frac{\pi}{T} t\right) R d t=\frac{Q^2 \pi^2 R}{8 T}$