Calculating Heat Loss From a Room of 125m3 - Confusing Results?

[TSN79]

A room is 5x5x5=125 m3 and holds a temp of 30C. On the other side of all the walls the air is 20C. I measure that the room temperature drops about 0.001C per second. If I now use this equation...

$$\dot Q = V \cdot C_P \cdot \rho \cdot \dot T$$

...I get the amount of heat that needs to be added in order for the room to keep this temperature (I think), and it's about 144W. What I don't get is that if I now calculate how much heat goes through the walls using the following equation...

$$\dot Q = U \cdot A \cdot \Delta T$$

...this comes to 300W, but that means that I'm actually losing 300-144=156 Watts more than the first equation tells me!

Am I getting something all wrong here?! This really confuses me, and all attempts to explain this to me will be appreciated.

 

[Q_Goest]

The two equations are valid. I assume you're doing this experiment on a room and finding some discrepencies, is that correct?

If so, I'd guess that one or more of the constants you're using is off. It would be very difficult to accurately describe the overall $$C_P, \rho$$ or $$U$$ accurately.

Another problem may be overall heat transfer. Are you neglecting radiation heat transfer? Seems to me there would be some significant contributions due to the sun's heating.

 

[ravenprp]

It is understandable that you are confused by the results you are getting from these calculations. However, there are a few factors that may be contributing to the discrepancy in the results.

Firstly, the equations you are using are different and may be measuring different things. The first equation, \dot Q = V \cdot C_P \cdot \rho \cdot \dot T, calculates the heat that needs to be added to the room in order to maintain its temperature. This takes into account the volume of the room (V), the specific heat capacity of the air (C_P), the density of the air (rho), and the rate of change of temperature (\dot T). This equation is useful for determining the heating or cooling needs of a room, but it does not take into account the losses through the walls.

On the other hand, the second equation, \dot Q = U \cdot A \cdot \Delta T, calculates the heat loss through the walls of the room. This takes into account the overall heat transfer coefficient (U), the surface area of the walls (A), and the temperature difference between the inside and outside of the room (\Delta T). This equation is useful for determining the insulation needs of a room, but it does not take into account the heat needed to maintain the temperature inside the room.

Secondly, there may be other factors affecting the heat loss through the walls that are not accounted for in the equations. For example, the type and thickness of the walls, the presence of windows or doors, and the outside temperature can all affect the heat loss through the walls. These factors may not be accurately reflected in the equations you are using, leading to discrepancies in the results.

In conclusion, it is important to understand the limitations and assumptions of the equations you are using and to consider all factors that may affect the heat loss in order to get a more accurate result. If you are still unsure, it may be helpful to consult a professional or do further research on the topic.