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."
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….
Best Answer
Your first question. We assume that the heat flow (mainly by convection)between water and calorimeter is rapid enough to maintain equilibrium – implying equal temperatures throughout. This won't be quite true.
[I forget who it was, about 200 years ago, who found that a container of stewed apple cooled much more slowly than the same mass of water in the same container. He wrongly concluded at first that the specific heat capacity of stewed apple was much greater than that of water. He'd forgotten that there won't be any convection (or conduction) to speak of in stewed apple, so the container would rapidly become much cooler than the middle (I almost said 'core') of the contents. So the rate of heat loss was much less than what was expected from the temperature as measured in the middle.]
As for your second question, excess temperature in this context means temperature of cooling body minus temperature of surroundings.