Outline 4 #4A.9 -- Why is Water Negative?

[Jess Cooper 1C]

For 4A.9, the answer key says that the heat lost by the copper is gained by the water, which makes sense since the copper starts at a higher temp. But then why is the q of H2O not positive and the q of the copper negative?

The answer key says: heat lost by metal = - heat gained by water

[Justine Lim 3L]

Hi! I am not sure if this could answer your question, but I believe the location of the negative sign should not change the overall answer.

[jhb123]

Hello!

This has to do with the first law of thermodynamics. The heat lost by the metal is “transferred” (converted) and used to heat the water. The heat of the water, itself, is not negative. The negative sign is just suggesting that, in order to heat the water, the metal had to lose some amount of heat (q).

[Daniel Lee 2J]

I think the important part is that the signs are opposite, as this is also a matter of what perspective you choose for systems vs. surroundings. Additionally, the individual equations for each side actually take this into account. The textbook says "heat lost by metal" is positive because they include (Tf—100) in their equation. We know Tf for the metal will be lower than 100, so this would give us a negative value. This negative value would then be equal to the negative of the heat gained by water (if that makes sense) which checks out.