Heat Transfer into a 1000L container

[emericas2015]

Have been slightly racking my brains trying to remember the basics of this, but have a quick and probably pretty simple heat transfer problem. Was in a discussion

Two standard 1000 liters square enclosed plastic HDPE containers (1m x 1m x 1m).
One is filled up 800 liters (some air present at top)
One is filled up only to 200 liters (lots of air up at top)

Each tank is wrapped in a 2kW tank insulating heater blanket (around the sides). Tops and bottoms are also insulated (although no heat applied to those portions).

What are the heat transfer physics at play here? Which tank will heat up the fastest, but more importantly, scientifically why? My prediction was that it would be about equal due to the fact that although the filled tank is more mass, there is more surface area being heated through conduction of HDPE to water.

 

[Simon Bridge]

Have been slightly racking my brains trying to remember the basics of this, but have a quick and probably pretty simple heat transfer problem. Was in a discussion

Two standard 1000 liters square enclosed plastic HDPE containers (1m x 1m x 1m).
One is filled up 800 liters (some air present at top)
One is filled up only to 200 liters (lots of air up at top)

Each tank is wrapped in a 2kW tank insulating heater blanket (around the sides). Tops and bottoms are also insulated (although no heat applied to those portions).

What are the heat transfer physics at play here?

Entirely internal ... no heat sources are provided, and temperatures of the materials is not given.

Which tank will heat up the fastest, but more importantly, scientifically why?

Neither - no heat source and no temperature data. Just wrapping something in a blanket does not heat it up.

My prediction was that it would be about equal due to the fact that although the filled tank is more mass, there is more surface area being heated through conduction of HDPE to water.

You are proposing that the temperature outside the container/insulation is higher than the temperature inside, and the insides are initially at the same temperature?
Then heat initially flows equally into both materials ... a quick and dirty calculation for how fast the temperature climbs will follow the heat capacities ... water heats up much slower than air. The tank with the most air will likely get warmer sooner.
If you think about it - put two pots in the oven, different amounts of water in each pot: which pot will boil first?

If the tanks are next to each other ... then they can exchange heat depending on the proximity.