# What does the area under the curve of a temperature-time graph represent?

I’m trying to calculate the total heat produced by a system over a period of time and I’ve gotten a regression line of y= log x to represent the best produced by the system. To calculate the total heat produced by the system, would it be valid to take the integral of log x? And if this is valid, what would be the units of the area under the curve?

• What is "x" in the equation? Jan 22, 2019 at 22:17
• @BobD x represent time while y is the temperature Jan 24, 2019 at 2:38

If what you're trying to describe is a thermally isolated* system which is gradually heating up, and if your axes are temperature and time, then the total amount of heat $$Q$$ produced after a given amount of time is related to the temperature $$T$$ through the definition of heat capacity:
$$Q(t)=C(T(t)-T_0)$$
for a system with heat capacity $$C$$ and initial temperature $$T_0$$. Taking the integral will give you an unrelated quantity; the relevant operation is taking the temperature difference between the initial and final times.