Answer
$8.16\times 10^6~J~~$ of thermal energy is produced in the cup in 1.00 hour.
Work Step by Step
We can use the kinetic energy after accelerating through the potential difference to find the ion's speed:
$K = \vert q \vert~V_1$
$\frac{1}{2}mv^2 = \vert q \vert~V_1$
$v^2 = \frac{2~\vert q \vert~V_1}{m}$
$v = \sqrt{\frac{2~\vert q \vert~V_1}{m}}$
$v = \sqrt{\frac{(2)(3.20\times 10^{-19}~C)(1.00\times 10^5~V)}{3.92\times 10^{-25}~kg}}$
$v = 4.04\times 10^5~m/s$
The thermal energy will be equal to the kinetic energy of the material.
We can find the kinetic energy of the material:
$K = \frac{1}{2}mv^2$
$K = \frac{1}{2}(100\times 10^{-6}~kg)(4.04\times 10^5~m/s)^2$
$K = 8.16\times 10^6~J$
$8.16\times 10^6~J~~$ of thermal energy is produced in the cup in 1.00 hour.
