Delta T in Calorimetry always positive?

In summary, it is important for ΔT to be positive in part number 5 to ensure that the heat is flowing in the correct direction and to uphold the second law of thermodynamics. This is achieved by defining Q(gain) and Q(lost) in a way that always results in a positive difference in temperature. Alternatively, the equation can be rearranged to make Q(gain) positive and Q(lost) negative.
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RaulTheUCSCSlug
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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?
 
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RaulTheUCSCSlug said:
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(Tf - Ti). 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.
 
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1. Why is Delta T always positive in calorimetry?

Delta T, or change in temperature, is always positive in calorimetry because it represents the difference between the final and initial temperatures of a system. Since temperature is a measure of thermal energy, it can only increase or decrease, resulting in a positive change.

2. Is Delta T always positive even if the system loses heat?

Yes, Delta T is still positive even if the system loses heat because it is a relative change in temperature. Even if the final temperature is lower than the initial temperature, the change is still positive as long as there is a difference between the two temperatures.

3. Can Delta T ever be negative in calorimetry?

No, Delta T cannot be negative in calorimetry because it represents the difference between two positive values (final and initial temperatures). Negative temperatures do not exist in reality, so Delta T will always be positive.

4. How does Delta T relate to the amount of heat exchanged in a system?

Delta T is directly proportional to the amount of heat exchanged in a system. This means that the larger the change in temperature, the more heat was exchanged. However, Delta T alone does not provide information about the specific amount of heat exchanged, as it also depends on the heat capacity of the substances involved.

5. Can there be exceptions to Delta T always being positive in calorimetry?

In most cases, Delta T will always be positive in calorimetry. However, there may be exceptions in certain scenarios, such as when a substance undergoes a phase change (e.g. melting or boiling). In these cases, the change in temperature may be considered 0, resulting in a Delta T of 0.

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