# How room temperature will change in 1 hour

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1. Aug 9, 2015

### baracoda

Hello, having the following data can I somehow calculate how will the temperature in room change in 1 hour time?

room lenght = 6m
room width = 6m
room height = 3m

lets say radiator is 0.5m x 1.5m and has 2000W and it can be in 2 states: on/off

I have also the current air temperature and relative humidity.

It is just a hipothetical question so I can assume some needed parameters if necessary.

2. Aug 9, 2015

### Staff: Mentor

It will depend on the walls and the interior.
Air has a specific heat capacity of 1J/(g*K), heating it alone with 2000 W would create a sauna. That's not what happens, of course. The solid objects in the room will absorb most of the heat.

3. Aug 9, 2015

### Staff: Mentor

If you use the specific heat capacity, multipy by the energy input and divide by the mass of air (or volume and density...), your answer won't be too far off for the first hour or two. After that, though, it will start to diverge quickly from the reality as other factors such as the heat absorbed by the objects in the room and the walls...and heat transfer through the walls becomes significant.

4. Aug 10, 2015

### Staff: Mentor

I have worked in rooms that size, with 2 kW heating. If they would have raised the temperature to 100 °C within one and a half hour, I would not have worked in those rooms!

5. Aug 10, 2015

### Staff: Mentor

One of us did the calculation wrong because that's not the answer I got...

6. Aug 10, 2015

### CWatters

While you put energy into the room some is escaping through the walls and via ventilation. Depending on the temperature inside and out and how well insulated it is, it might take more than 2kW to maintain a temperature let alone increase it.

The static temperature case (power in = power out) is usually easy to work out if you have data on the thermal properties of the walls, windows and ventilation. The dynamic case isn't quite so easy.

7. Aug 10, 2015

### Staff: Mentor

My calculation is linked in post #2.

8. Aug 10, 2015

### sophiecentaur

Your calculation needs to include area of surfaces, rate of air change, distribution of 'warm' air in the room (what actually 'feels warm'). There are many links which discuss the practicalities involved (from the point of view of Heating Engineers. If you want a realistic answer, it may be worth reading a few as it's easy to miss factors out if you are trying to start from scratch and just use 'theory'.

9. Aug 10, 2015

### Staff: Mentor

Whoops, I couldn't understand the funky units WA used, so I had to re-create it manually; I messed-up the time conversion and was low by a factor of 60.

The result is more surprising to me than it should be, but in any case means the divergence from the simple case (when heat transfer and heat capacity of objects in the room starts to matter) happens in just a few min.

10. Aug 10, 2015

### Staff: Mentor

Right. This is easy to test during the winter: open a window => it gets cold within minutes. Close it => ten minutes later, it is warm again (if you don't use a thermometer, leave the room as slow gradients are hard to notice). The short air exchange doesn't cool down the walls and other things, so once the window is closed they quickly re-heat the air in the room.

11. Aug 10, 2015

### baracoda

Thank you guys for the responses!

What do you think of the following way of thinking:

1. I can calculate the amount of energy necessary to heat up the air:
$$W=mc_{air}\Delta T$$
mass of the air enclosed in the room:
$$m=\rho V$$
$$m=6*6*3*1.2=216\left [ kg \right ]$$
specific heat capacity:
$$c_{air}=1005\frac{J}{kgK}$$
temperature difference (lets say now it is 20 Celsius degrees in the room and I want to heat up to 23):
$$\Delta T=3K$$
So summing this up we have:
$$W=216kg*1005\frac{J}{kgK}*3K=651240J=0.1809kWh$$
I have a heating system with power 2kW so in order to get 23 Celsius degrees I need to heat it for the following time:
$$\frac{W\left [ kWh \right ]}{P\left $kW \right$}=\frac{0.1809}{2}=0.09\left [ h \right ]=5.4\left [ min \right ]$$

What if I somehow use it for calculating how everything will change in 1h? Is the solution ok?

P.S. 2kW heater was just an example.

12. Aug 10, 2015

### CWatters

Is this a real world problem or just an exercise?

Real houses are ventilated and leak air quite badly. Some ventilation is also required by local regulations. This can be >0.6 air changes an hour. Quite a % error if not taken into account. Losses through walls and windows can be equally significant.

13. Aug 10, 2015

### Staff: Mentor

That's the calculation I linked to in post #2. It works for very short timescales (a few minutes) only, afterwards you have to take into account that the rest of the room (with much more mass than the air) will heat up as well.
By the way, the density of air is not 1kg/m3.

14. Aug 10, 2015

### baracoda

No it is just an excercise. I am a programmer and I do not know physics. I am trying to figure out how to calculate how temperature will change in room during the hour (or other time span) and I want to skip the advanced parts of this problem, the easier for me to understand the better :)

Oh.. you are right. Sorry.

I have came up with such a model and I have given some parameters the default values . I am looking for a way to be able to calculate how the temperature will change in blue room in 1 hour if I will switch on the radiator or switch it off (or leave in the current state). Lets say the room is adjecent with 2 other rooms which temperature is 22 Celsius degrees. In the room there are also bed, wardrobe and desk with the dimensions given. Can you please help me to combine the @mfb solution with the situation below? Please do not take into consideration very sophisticated physical phenomena - it can be kind of controlled situation.

15. Aug 10, 2015

### Staff: Mentor

So, i'll repeat what the others said, in a different way:
In HVAC, the transient case you are investigating is usually totally ignored, because it has little real value. The steady-state case (balanced input and output heat) is what matters.

So can you explain what value the answer to your question will provide to you? What are you going to use this for?

16. Aug 10, 2015

### baracoda

If I understand correctly, those changes I am trying to calculate are more or less right in situation: it is very cold in the room, I am switching on the radiator, and after one hour the temperature is x. Then those changes are not so big, and the other things in the room, together with walls etc play bigger role? Is that right? So is there any way to somehow incorporate the data I have put int the picture to calculate those temprature changes? I dont expect the exact perfect result, just more or less know how it behaves.

Sure, I am trying to write sth like a simmulator - an application which uses machine learning algorithms for my classes. I thought that a heating simmulator would be a good idea. So one part of the task is just to calculate how the temperature will change after one hour. It should be a very simple case as it is not the main part of the project.

17. Aug 10, 2015

### Staff: Mentor

It is really hard to get a realistic model purely with theoretical predictions. Putting an actual heat source is a much better way to estimate how a room will react as there are so many factors that influence the temperature changes significantly.

18. Aug 10, 2015

### baracoda

I see... there are many factors that influence the result...

You mean, that using the solution you have proposed in the first post would be the best idea? If yes can you please advise me how many Wats approximately the radiator should have to be near to realistic solution? And is there also some kind of easy way to calculate how much the temperature will drop if I will switch off this radiator?

19. Aug 10, 2015