What kind of model should I use to express temperature change in my experiment?

[TSN79]

For a normal population growth we have the basic equation

$${{dP} \over {dt}} = kP$$

I'm not investigating pop.growth, but temperature change, but it really shouldn't matter if I'm measuring degrees instead of people. The only problem I have is that this equation only seems to be fairly accurate if there is a general increase in the values as it goes along. In my experiment a room is heated for 24h, and I want to express the temperature change using the following set of equations:

$$Q_P + \rho \cdot C_{P,Air} \cdot \dot V\left( {T_O - T_R } \right) = U \cdot A\left( {T_R - T_O } \right)$$

and

$$m \cdot C_{P,wall} \cdot {{dT_m } \over {dt}} = U \cdot A\left( {T_R - T_m } \right)$$

I haven't done the experiment yet, but I'm not convinced that the temperature will always increase steadily, it might decrease in periods, and increase in others. What kind of model should I then use?

Of course, if the temperature does indeed turn out to only have a slow steady increase and no decrease, then there won't be a problem.

 

[Emieno]

That way of solving your current problem complicates everything, I suggest statistical analysis to then predict the changes in temperature instead. By the way, a dot on the V's head doesn't look right to me.

 

[tacman]

Based on the information provided, it seems like you are conducting an experiment to measure temperature change in a room over a period of 24 hours. In this case, it would be more appropriate to use a different model than the one for population growth.

One possible model that could be used is the heat transfer equation, which takes into account the various factors that affect temperature change such as heat flow, thermal conductivity, and specific heat capacity. This model would be more suitable for your experiment as it considers the specific conditions of your setup, including the heating of the room and the materials used in the walls.

Alternatively, you could also consider using a regression model to analyze your data and determine the relationship between the different variables in your experiment, such as time and temperature. This would allow you to identify any patterns or trends in the temperature change over the 24-hour period.

Ultimately, the most appropriate model to use will depend on the specific details of your experiment and the type of data you are collecting. It may be helpful to consult with a statistician or research advisor to determine the best approach for your particular experiment.