In an effort to understand more about the first law I was wondering about the potential energy term and how it would influence the gas inside the box I made this question and tried to answer it.
I will assume that the air follows the ideal gas law, there is no air resistance and the box stops moving immediately when it reaches the rigid ground.
The first law: $$ 0 = \Delta PE + \Delta U\\ gH = c_v (T' - T)\\ T' = gH/c_v + T $$
would this be correct or missing something? (i.e. invalid assumptions..)
I am also wondering if the energy is fully transferred to the ground instead..