you are not supposed to put anything warm into a fridge as it raises the fridge temperature allowing bacteria to grow
Well this is an interesting sciencey question so lets look at it a bit more closely. It's certainly true that putting anything in a fridge which is warmer than the ambient temperature will not only cool it but also cause the temperature of the fridge to rise slightly until the cooling regulation of the fridge can extract the added heat. However it is also certainly true that when a butterfly lands on Tower Bridge the bridge bends through by an infinitesimally small amount. Likewise putting an egg in a fridge the effect will be very small and generally the temperature rise effect will be dependant on several factors, off the top of my head these will be.
Specific thermal capacity of the 'hot' object X It's weight (or more properly mass) X it's temperature
The thermal capacity of the fridge and it's contents (as above, Specific Thermal Capacity X mass X temperature)
The sensitivity of the controlling temperature regulator and the fridges cooling capacity.
These are just first order variables which effect the problem and a more accurate transient analysis would need to consider the cooling effiency the airflow and how the fridge was packed the position of the egg in the fridge and it relationship to food which might be effected by raised temperature and so on and so on. But just taking a very simple steady state case based on thermal energy. A new laid egg lifted from under a chicken and taken to a fridge will be around say 35degC maximum and weigh 65grams the fridge ambient temperature will be around 5degC and basing the mass of it's contents on my fridge one third full of food with the same thermal capacity of an egg (ie a third full of eggs. I know this isn't real world but as an illustration), I calculate a steady state rise in temperature of 0.012 degC. So you would need to add a lot of eggs at hen body temperature to raise the temperature by a measurable amount let alone a significant amount.
This is a simple calculation however which doesn't include the thermal capacity of the walls of the fridge and it's cooling efficiency (ie ability to extract heat via it's cooling mechanism) both of which would further reduce the rise. However it doesn't include the local transient effects which will cause adjacent food to rise in temperature to a greater extent whilst the heat is conducted and convected away. To estimate a very simple absolute maximaum effect of this this imagine that the egg is completely surrounded by other eggs at fridge temperature and the heat lost from hot egg is first 'shared' by conduction with the adjacent 28 eggs (for arguments sake) they would have a temperature gradient across them, however again taking a simple steady state case and discounting heat lost from the surrounding eggs, they would rise in temperature by about 0.8degC. This is a gross simplification and a real case would be much lower than this and wouldn't last long before the heat spread and the temperature fell again.
The worst effect of putting a warm egg in the fridge is the effect of losing a volume of cold air when the door is opened which will be replaced by warm air at room temperature. Using my fridge as the model and the case above, when I open the door 2/3rds of it's volume of cold air literally tumbles out and I calculate this to be 406 grams of air at 5degC. This is replaced by 320grams of air at 25degC (same volume but less dense). Air has roughly half the specific heat (heat capacity) as water (an egg) so this is approx equivalent to me putting 160grams of eggs (2.4eggs) at room temperature in or 1.6 eggs at the 35degC hen body temperature in the fridge.
Are you following all this?
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If not the bottom line is the effect of adding new laid warm eggs from a chicken is negligible and a single egg will cause a temp rise of far less than a tenth of a degree C. Effectively putting 1 doz warm eggs in my example fridge is has the same effect as adding 1and a half dozen room temperature eggs. Just opening the door will have about the same effect as adding two warm eggs so if you put in the ambient temp eggs but wait for the warm ones to cool first thus opening the door twice you'd better have three or more eggs at 35degC before that might show any theoretical benefit in the slightest.
Well I hope that clears it up??
Now for the urban myth about hot water freezing quicker than cold water..........hey hey come back... you've all logged off!!!
HF