I am reading about Newton's Law of Cooling and the following is an extract from my textbook on the experimental verification of this law.

*"Consider a spherical calorimeter of mass m whose outer
surface is blackened. It is filled with hot water
of mass m1. The calorimeter with a
thermometer is suspended from a stand.
The calorimeter and the hot water radiate
heat energy to the surroundings. Using a stop
clock, the temperature is noted for every 30
seconds interval of time till the temperature
falls by about 20o C. The readings are entered
in a tabular column.*

*If the temperature of the calorimeter and
the water falls from T1 to T2 in t seconds, the
quantity of heat energy lost by radiation
Q = (ms + m1s1) (T1 – T2), where s is the
specific heat capacity of the material of the calorimeter and s1 is the
specific heat capacity of water.*"

[Calculations][1]

I have the following doubts:

1) How can the temperature of both the water and the calorimeter fall from temperature T1 to T2 ? If the initial temperature of the hot water is T1, then is it assumed that the temperature of the calorimeter is also T1 ? Even so, won't their rates of cooling be different ?

2) What exactly is the " mean excess temperature" ? This is the definition I found online:

"Excess Temperature is defined as the temperature difference between heat source and saturation temperature of the fluid."

But my textbook says nothing about this 'saturation temperature'.

I apologize if this is too long. But I couldn't find much information online....


  [1]: https://i.sstatic.net/1Wc1B.png