Which reactions are negative and positive when solving for heat?

[AndresElizarraras 2A]

Textbook question 4A.9 asks

"A piece of copper of mass 20.0 g at 100.0 C is placed in a vessel of negligible heat capacity but containing 50.7 g of water at 22.0 C. Calculate the final temperature of the water. Assume that no energy is lost to the surroundings"

The textbook manual sets up the equation "heat lost by metal = - heat gained by water"

I understand why we're setting up the equation, but why is the heat gained by the water negative? Would it not make sense for the heat lost by the metal to be negative since it's exothermic & releasing energy?

[Mace Drobac 1E]

I think it is saying that the heat gained by water is positive. Multiply that by -1 and you get the change in heat for the metal (which is negative).

[Nina Vu-Gia 1C]

The heat gained by the water will be a positive number. However, the heat lost by the metal will be a negative value because "losing heat" or "releasing heat" is an exothermic process and is therefore a negative number. So, for example, if the metal lost 25 degrees C of heat and therefore water gained 25 degrees C of hear then, without the negative it would be: -25 = 25 --> which obviously is not equal. The negative sign in front of the water is just to show the relationship between the values.

[Camilla Hinrichsen 1A]

Heat gained by the water is positive, because heat being gained is an endothermic reaction. Heat being lost from metal will be negative because if the heat is being lost from the metal, it is an exothermic reaction because you're losing heat. A helpful tool I like to use is "endo" is like "enter", which means that you will gain heat in an endothermic reaction, and "exo" is similar to "exit" which means you lose heat in an exothermic reaction.

In this problem specifically, it is showcasing that if you negate the change in heat gained by water (a positive number), you will get the change in heat lost from the metal (a negative number)

[Natalya Cummings 2E]

This problem relies on the idea of conservation of heat—it can't be created or destroyed, only transferred. Thus, a change in temperature for the metal is also going to result in a change of temperature in the water, and these changes will be the same but have opposite signs.