[narutodemonkill]

you mix 20.5 g of water at 66.2 degrees celsi
us with 45.4 g of water 35.7 degrees Celsius in an insulated cup what maximum temperature of solution after mixing

6.98. The heat gained by the water at the lower temperature equals the heat lost by the water at the higher temperature. Each heat term is s x m x Δt. This gives
 
(4.184 J/g•°C)(45.4 g)(  tf −  35.7°C)  =  (4.184 J/g•°C)(20.5 g)(66.2°C  −  tf) The specific heat and the units can be canceled from both sides to give
(45.4)(  tf−  35.7°C)  =  (20.5)(66.2°C  −  t)
After rearranging, you get 65.9 t
 = 2977.88. This gives t
 45.2°C.

****My question is why is it (66.2-tf) and not (tf-66.2) it does not make sence because change in temp=tf-ti
and they wrote it as if 66.2 was temp initial

[narutodemonkill]

you mix 20.5 g of water at 66.2 degrees celsi
us with 45.4 g of water 35.7 degrees Celsius in an insulated cup what maximum temperature of solution after mixing

6.98. The heat gained by the water at the lower temperature equals the heat lost by the water at the higher temperature. Each heat term is s x m x Δt. This gives
 
(4.184 J/g•°C)(45.4 g)(  tf −  35.7°C)  =  (4.184 J/g•°C)(20.5 g)(66.2°C  −  tf) The specific heat and the units can be canceled from both sides to give
(45.4)(  tf−  35.7°C)  =  (20.5)(66.2°C  −  t)
After rearranging, you get 65.9 t
 = 2977.88. This gives t
 45.2°C.


was it just so the + - signs could be balanced?
****My question is why is it (66.2-tf) and not (tf-66.2) it does not make sence because change in temp=tf-ti
and they wrote it as if 66.2 was temp initial