Textbook 4A.9

[Antonia Valencia 2H]

Hi! When trying to solve this question, I found myself a bit confused about how we were supposed to know that "the heat lost by the metal = -heat gained by the water" and I additionally was a little bit confused by what it means. Does it relate to the qsys = - qsurr relation discussed in lecture? Moreover, is it basically revealing that the amount of heat gained by the water is essentially equal to the amount of heat lost by the metal (and it would be a negative value because that heat was lost)? Thanks so much for the help!

[Lawrence Tran 2H]

Yes, you basically understand it already! "The heat lost by the metal = -heat gained by the water" is just the qsys = -qsurr equation applied to this particular scenario, and you're right in saying that it means the amount of heat gained by the water is equal to the amount of heat lost by the metal.

[WendyN_L2]

The idea of heat lost by copper = -heat gained by water, follows the first law of thermodynamics, that means the energy must be constant in a general sense "change of energy in system + change of energy in surroundings = 0 = energy change as a whole". To apply it to this context and maneuver this equation you get "change of heat in the copper = - change in heat in the water." It is same concept to what was said during lecture. Hopefully this kinda helps