## HW 8.21

$\Delta U=q+w$

JennyCKim1J
Posts: 51
Joined: Fri Sep 29, 2017 7:04 am

### HW 8.21

For 8.21, why is heat lost by metal = - heat gained by water? Feels like it should be: since metal (Cu) is the system, so - heat lost by the system (metal) = heat gained by water. Why are the signs flipped?

Abel Thomas 2C
Posts: 31
Joined: Fri Sep 29, 2017 7:06 am
Been upvoted: 1 time

### Re: HW 8.21

Well the negative sign could be on either side of the equation and it would still be correct. However, the problem is asking for the final temperature of the water. Thus, for the purpose of writing the equation to solve the problem, it is stated that heat lost by the system (metal) = - heat gained by water.

Nora Sharp 1C
Posts: 53
Joined: Sat Jul 22, 2017 3:00 am

### Re: HW 8.21

Given that the final temperature of the metal will be less than the initial, the calculated energy lost by the metal will be negative. And given that the final temperature of the water will be more than its initial, the calculated energy gained by the water will be positive.

So before modifying the equation with that minus sign, this is what we've got:
energy lost by copper (negative value) = energy gained by water (positive value)

The sign next to copper is already negative, because the nature of the formula we use to calculate it already takes into account the fact that the copper piece lost energy. By multiplying it by a negative sign, we can account for that, setting the two values on either side of the equation equal to each other. If we didn't do that, the equation would be incorrect, as it would be saying a positive and a negative value are equal to each other. This is actually why we can multiply either side with the minus sign as Abel said (just not both) and get the correct answer. I don't really think it has too much conceptual significance; it's just something that helps us get the right answer.