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The definition of an exothermic reaction is one that gives off heat. In the case that delta T is positive, that is looking at the change in temperature with respect to the surroundings, because sometimes there is no appropriate way to measure the delta T of the system. An exothermic reaction as a system will give off heat to the surroundings, thereby increasing the final temperature of the surroundings. When reading the setup of the problem, make sure to not whether the delta T is referring to the system or the surroundings.
delta T is measuring the temperature outside of the system. While delta H is measuring in terms of the system inside. So in an exothermic reaction, delta H would be negative but delta T would be positive. And in an endothermic reaction, delta H would be positive, but delta T would be negative.
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