FInding Final Temperature

Question

You probably know that when two objects at different temperatures are brought into contact, heat always travels from the hot to the cold, never the reverse. Imagine then that you have two gold metal blocks, one with mass 390.0 grams at a temperature of 126.0deg C and another with mass 329.0 grams at a temperature of 37.5deg C that are brought into contact in a perfectly insulated container.The specific heat of gold = 0.129 JK-1g-1.

What is the final temperature when the two blocks come into thermal equilibrium in the insulated container?

Please help. Could you please show me how to do this

Answer 1

390.0 grams at a temperature of 126.0deg C , &

another with mass 329.0 grams at a temperature of 37.5deg

-------

what we do is to calculate the energy that the hotter one has "due to the amount that it is hotter", that's the 390 gram block & it is 88.5 degrees hotter than the colder one:

dH =mCdT

dH =390grams (0.129 J/K-g)(88.5 degrees)

dH = 4452.4 Joules

this 4452.4 Joules Joules is excess energy, if both metals were cold @ 37.5 C , I could add this energy back to them( all 719.0 grams of gold), ,... and they will heat up to the same temperature that they would have equilibrated to on their own if I ran it the way the experiment related

dH = mCdT

4452.4  Joules = 719.0 grams ( 0.129J/g-K)(dT)

dT = 48 degree Celsius

this tells us that if we reintroduced the 4452 Joules to the 719 grams of gold @ 37.5 Celsius,... the temperature would rise by 48 degrees,(37.5 plus 48 --> 85.5 Celsius)

your answer is: 85.5 Celsius is the final temp