Let's say we want to freeze a banana. Would it freeze faster if we insert it into an empty freezer, or into one that already contains many frozen bananas?
[Physics] Does a full freezer freeze items faster than an empty one
everyday-lifethermodynamics
Related Solutions
based on casual observation, believes that coffee will cool faster than ordinary hot tap water
Let's revisit the "casual observation" part. Are the initial conditions the same? Water from a kettle will usually be hotter than from a coffee machine. And we tend to do things to coffee that we don't do to water, like add 10% of another liquid (milk) at low temperatures, a dissolvable solid and considerable agitation with a cold metal heat sink. So it is highly likely that the coffee is much cooler than hot water 2 minutes after preparation, but it's nothing to do with the inherent properties of coffee.
The density of water rises from 0 to 4 degrees celsius. So you would have a gradient of water temperatures. On the bottom 4 degrees celsius and colder water above it. This is also the reason why fish survive in winter, they just dive to the bottom where the temperature stays warm longer. Also the density of ice is smaller than water so it will float.
Best Answer
Heat Capacity
You are comparing two situations, and to formalize this, let's say that the freezer has a given volume, $V$ and that volume is broken down into air and other frozen materials. Then we have the situation that $V=V_{air}+V_{stuff}$. The heat capacity of the entire freezer between the two situations will be vastly difference because the volumetric heat capacity for air and ice (which is the most common item included in "stuff") is vastly different by a factor of about 1000. I'll use the Wikipedia notations, where specific heat capacity is $c$ ($\frac{J}{kg K}$) and volumetric heat capacity is $c \rho$. The volumetric heat capacity times volume is the heat capacity (denoted $C$) so for the entire freezer we have the following.
$$C = \left(V c \rho \right)_{air} + \left( V c \rho \right)_{stuff}$$
The heat capacity matters because should you insert some mount of heat into the freezer, $Q$, then after equilibrium is reached, the temperature will raise by:
$$\Delta T = \frac{Q}{C}$$
So if we don't consider the work of the freezer thermal cycle actively cooling the air, then the freezer with more stuff in it will cool the item faster because the temperature of the air+stuff changes less, so the $\Delta T$ in the Newton cooling model will be greater and it will cool faster and cool to a lower temperature.
Air Cooling
It is relevant to note that the air is actively cooled by the freezer systems and the stuff is not. This is interesting because it will have relevance to the heat transfer mechanisms (more later). Although this isn't entirely correct, we could assume that the cooling device takes some flow rate of air continuously, $\dot{m}$ (kg/s), and cools with some enthalpy change, $\Delta h$ (J/kg). That enthalpy change removes heat from the system, but that doesn't change from one case to the other.
But that can't be the full picture. Heat is only removed from the freezer if the temperature drops below a certain value. So, another way to do this may be to assume that the cooler keeps the air at a certain temperature, but that may defeat the purpose of the problem. It is also possible that the thing being cooled, in fact, outpaces the cooling device and heats the air faster than it can be cooled. In that case the air temperature would rise above the programmed setpoint and stay there until the item being cooled started to approach the freezer temperature.
Heat Transfer Mechanisms
There are two mechanisms of heat transfer between the item you are freezing and other stuff in the freezer.
Obviously, the 1st one transfers with the air and the 2nd one transfers with the stuff. I would like to propose several simplified models such that we can talk more specifically about predictions.
As I've said already, number 1 clearly has the freezer with more stuff win. Number 2 could potentially go in the direction of the freezer with less stuff because of the larger heat capacity of air (which will only work for a small item), but the radiative heat transfer still advantages the case with more stuff. In number 3 the freezer with more stuff clearly wins unless the flow path for convection is restricted.
The exact one that will win does depend on the specific values for the system, so that's in the hands of the experimentalist. Generally though, the higher heat capacity and the ability to transfer heat through radiative transfer is likely to favor the freezer with more stuff in it.