We know that $C$=$mc$ Where($m$ is the mass of the body and $c$ is the specific heat) , A body
$M_1$ with $C_1$ and another body $M_2$ with $C_2$ where ($C_1$ $\gt$ $C_2$), What is the reason that when they touch heat is transferred from $M_1$ to $M_2$ ? Let me give an example so it's easier to understand what I mean :
0.25 kg of water at 20'C is mixed with 4 kg of aluminum at 26'C and 0.1 kg of copper at 100'C the finial temp of the three materials is ...
Here there might be 3 probabilities: 1 -The final temp 26<$T$<100 , 2- 20<$T$<26 3- $T$=26 . Here we can predict where the final temp using $C$ of each element , $C_{water}$=1.0456 , $C_{Al}$=3.6 , $C_{Cu}$=0.0367 and since $C_{Al}$ $\gt$ $C_{water}$ $\gt$ $C_{Cu}$ ,we can predict that it will lie between the elements with the largest 2 heat capacities Aluminum and water 20<$T$<26 then we will be able to solve the problem correctly .
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1$\begingroup$ What are the temperatures of the two bodies? $\endgroup$– garypCommented Dec 22, 2021 at 12:21
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4$\begingroup$ This is simply not true. Heat flows from the hotter body to the colder one, regardless of their heart capacities. $\endgroup$– VercassivelaunosCommented Dec 22, 2021 at 13:14
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2$\begingroup$ I second the above comment by Vercassivelaunos. Your question as it is stated is irrelevant to heat capacities. Heat flows from hot to cold as described by the 2nd law of thermodynamics, dummies.com/article/academics-the-arts/science/physics/… $\endgroup$– Markoul11Commented Dec 22, 2021 at 16:39
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$\begingroup$ What i mean is it always true that when there are 3 bodies mixed the final temp of the mixture will lie between the temp of the 2 bodies of the higher heat capacities , why is that ? $\endgroup$– Youssef MohamedCommented Dec 22, 2021 at 18:40
2 Answers
It is not generally true that heat is transferred from $M_1$ to $M_2$. Suppose, for a counter-example, that both bodies are made of water so $c_1=c_2$ and suppose further that $m_1=2 \text{ kg}$ and $m_2=1\text{ kg}$ so we have $C_1>C_2$. Now, if $M_2$ is hot and $M_1$ is cold then heat will transfer from $M_2$ to $M_1$, not the other way around. It is their temperatures that determine the direction of heat transfer, not their heat capacities.
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$\begingroup$ look at the edit to understand what I meant $\endgroup$ Commented Dec 22, 2021 at 16:19
What is the reason that when they touch heat is transferred from $M_1$ to $M_2$ ?
Heat transfer is not based on the difference in heat capacities. It is based on a difference in temperatures. If the temperature of $M_2$ is greater than the temperature of $M_1$, heat will transfer from $M_2$ to $M_1$, in spite of the fact that the heat capacity of $M_1$ is greater than $M_2$.
,we can predict that it will lie between the elements with the largest 2 heat capacities Aluminum and water 20<$T$<26 then we will be able to solve the problem correctly.
You do not need to predict the final temperature will be between the two largest heat capacities to solve the problem. What would you do if all the heat capacities were the same? What's more, the final temperature may not be between the two largest heat capacities. It depends on the combinations of heat capacities and temperatures.
In your example the final temperature (which I calculate to be 25.3 C using the equation below) happens to be between the two largest heat capacities. But suppose we have 1 kg of copper instead of 0.1 kg so that its heat capacity becomes 0.367 instead of 0.0367. This results in more heat being available to transfer from the copper to the combination of the water and aluminum. Then, since the total heat transfer is zero for conservation of energy, we have
$0.367\Delta T+1.045\Delta T+3.6\Delta T=0$
$0.367 (T_{f}-100) + 1.0456(T_{f}-20)+3.6(T_{f}-26)=0$
$T_{f}=30.2 C$
Which is clearly not between the temperatures of the two largest heat capacities, which are still the water and aluminum.
Hope this helps.