The ratio gets better, but of course you have a lot more surface area! That naturally increases faster than the ratio improves, otherwise, beyond a certain size, you wouldn't lose any energy anymore.
V ~ r³, A ~ r². V/A grows faster than A. Heat losses relative to the volume become infinitely small for an infinitely large storage (this is the theoretical limiting case).
Absolute losses increase with size.
Yes, that's true, but be careful, in my opinion the interesting aspect is the losses relative to the stored heat. The source term of the balance (the heat electrically supplied through the heat pump should be independent of the surface-to-volume ratio) is, in my opinion, irrelevant here.
Background: I'll try it textually:
dQ/dT = k.A.dT, where
dQ/dt = cp.rho.V.dT/dt; after integration, this results in (
Tend -
Tstart)/(
Toutside -
Tstart) = exp(
-k.A.t / rho.cp.V). That means the time
t after which the contents have assumed the ambient temperature depends on V/A. And V/A gets larger the bigger the container is.
I log the operation of the heat pump on a Rasp.pi
Does your heat pump have a suitable interface or do you have to tinker to get it? Is there something like that for engineers as well (i.e., in Excel)?