Comparative energy efficiency of appliances

I have a general question about the comparative energy efficiency of a common electric stove heating element and a common electric refrigerator. Let’s presume that they are both about 5 years old. Let’s also presume that we are starting with an empty refrigerator that has been on for enough time so that it’s temperature is stabilized at a medium setting. Let’s also presume that I use the electric heating element as efficiently as possible, that is, by using a covered pan and by leaving the pan of water on the element until the residual heat in the element and temperature of the pan equalize. So then, let
s say I start with a pan of water of a given temperature, say 55 degrees Far. I heat that water on the stove and then place it in the refrigerator until it has returned to 55 degrees. I want to know which appliance will probably consume more energy, and by approximately how much.

There suspect that there must be specific energy efficiency data available to answer such a question but I wouldn’t know how to read and interpret the BTU’s and Watts over time numbers.

In general, it takes more energy to cool something off than to heat it up.

When heating something, no waste heat is generated - the entire purpose of the operation is to generate heat. Electric heating elements are quite efficient at transferring their energy into a pot of boiling water.

When cooling something off, you have to move the heat, plus the machinery will generate waste heat as a consequence of its own operation.