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Homework Statement
Material X,which is at a higher temperature, and Mercury are brought into contact for some time to allow heat transfer to take place.
CX : Heat capacity of Material X
θX : Temperature of Material X (At first)
CM : Heat capacity of Mercury
θM : Temperature of Mercury (At first)
θX is greater than θM. [ θX > θM ]
So heat energy is transferred from Material X to Mercury.
θN : Final temperature of both Material X and Mercury after heat transfer is complete. [ At thermal equilibrium. ]
Assumption: There is no heat loss to surroundings.
Homework Equations
Heat gained by mercury = Heat lost by Material X
δQM = - δQX
CMδθM = - CXδθX
CM(θN – θM) = - CX(θN – θX)
θNCM – θMCM = θXCX - θNCX
θNCM + θNCX = θXCX + θMCM
θN = [ θXCX + θMCM ] / [ CX + CM ]
The Attempt at a Solution
Therefore if we take X to be of different materials or even of different masses, the final temperature of the mercury , θN , should vary because the heat capacity of X , CX , changes. However this is not the case as if, for example, we place 2 mercury-in-glass thermometers in Ethanol at 50oC and Water at 50oC, both thermometers show a reading of 50oC.
Note: The Ethanol and the Water have different heat capacities.
I would like to see what you think about this problem. I really cannot understand, according to the above formula, why the thermometers show the same reading for the Ethanol and the Water. Any 2 other substances could have been taken but Ethanol and Water are simpler. Could someone please give me a good explanation about this?