as a chemist, love the analogy, resonates a ton with me. a little bit nit-picky, but:

"That is in addition to the actual cost of pumping the water from one tank to the other."

should be something like "that is in addition to the actual cost of lifting net 25 units of water higher".

The cost of moving from one tank to the other is, also heat loss, but the lifting part is recoverable.