Delta T in Calorimetry always positive?

[RaulTheUCSCSlug]

For part number 5, it says to make sure that each ΔT is positive. Why is this? Couldn't it be a negative? Or does it have to be positive since if it wasn't you would be getting heat going in the wrong direction? Like the one substance would be gaining instead of losing the heat? Which would violate the second law of thermodynamics, since entropy cannot be lowered?

 

[jtbell]

For part number 5, it says to make sure that each ΔT is positive. Why is this?

First, in step 2 they've written conservation of energy as "heat gained = heat lost".
Second, in step 3, Q(gain) and Q(lost) are defined so that the difference in temperature is always positive.

An alternative method would be to write conservation of energy as something like "total heat = 0", then define both Q(gain) and Q(lost) as mc(T_f - T_i). This would make a Q(gain) positive and a Q(lost) negative.

Your book's method basically moves all the Q(lost)'s over to the other side of the equation and changes their sign to make them positive.