(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Material X,which is at a higher temperature, and Mercury are brought into contact for some time to allow heat transfer to take place.

C_{X}: Heat capacity of Material X

θ_{X}: Temperature of Material X (At first)

C_{M}: Heat capacity of Mercury

θ_{M}: Temperature of Mercury (At first)

θ_{X}is greater than θ_{M}. [ θ_{X}> θ_{M}]

So heat energy is transferred from Material X to Mercury.

θ_{N}: Final temperature of both Material X and Mercury after heat transfer is complete. [ At thermal equilibrium. ]

Assumption: There is no heat loss to surroundings.

2. Relevant equations

Heat gained by mercury = Heat lost by Material X

δQ_{M}= - δQ_{X}

C_{M}δθ_{M}= - C_{X}δθ_{X}

C_{M}(θ_{N}– θ_{M}) = - C_{X}(θ_{N}– θ_{X})

θ_{N}C_{M}– θ_{M}C_{M}= θ_{X}C_{X}- θ_{N}C_{X}

θ_{N}C_{M}+ θ_{N}C_{X}= θ_{X}C_{X}+ θ_{M}C_{M}

θ_{N}= [ θ_{X}C_{X}+ θ_{M}C_{M}] / [ C_{X}+ C_{M}]

3. 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 , θ_{N}, should vary because the heat capacity of X , C_{X}, changes. However this is not the case as if, for example, we place 2 mercury-in-glass thermometers in Ethanol at 50^{o}C and Water at 50^{o}C, both thermometers show a reading of 50^{o}C.

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?

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: A very puzzling problem!

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