# Unheated intermediate room - positive or negative effect on flats temp. insulation?

This is a question I have heard quite some contrary opinions, so I want to ask it here, as it deals with physics in principle:)

The question is basically that, if having a unheated intermediate (in between) will reduce the insulation as compared to a direct outside wall?

This might be a little abstract so I will give the real case situation here:

Situation: I have a flat with:

• a) 1x a living room (is heated)
• b) 1x a kitchen (is not heated)
• c) 1x a small hallway-room in between a) b) (also not heated)
• b and c) are to be the "intermediate room" which the question refers to.

Further explained there are doors:

• One door between a) and b)
• Another between b) and c).
• the doors are closed.

As far as I understand given the basic situation above I assume that not heating the kitchen (nor the hallway) will not reduce the insulation. This is the insulation that the heated living room would have with regards to the outside world. In my opinion the temperature of the kitchen is not a matter for the insulation but only the characteristics of the outside walls.

This sketch shows the setup:

But differenly: Would start heating my kitchen help the insulation anything?
And to that extend: Would start heating my kitchen help me conserve heating cost (so if I heat room a "living" 100% in one case and in another I heat both rooms 50% and 50%?

I have done some thinking already and I am convinced that the question can be addressed physically. If nonetheless the question can be improved, please tell me how via comments. Else feel free and motivated to give the inside in an answer.

• You should not think in terms of "insulation" - what is important is the energy required to maintain a certain temperature in your room. Jan 25, 2014 at 20:50
• @guntbert thanks for the comment :) You suggest to look at the energy required to maintain a certain temp in that room. You mean Energy as in [kWh]/[Joules] right? or do you mean Energy per Unit of time so [kW]? ..... To give a reason why I was focusing on insulation is that I think the rate of Energy (in form of heat) leaving the room per Unit of time would depend on the insulation. Anyways if you can give an explenation of the effect of this intermediate room by refering to Energy that is aboslutely great. Looking forward! Jan 26, 2014 at 7:23
• I was talking about P (measured in W) needed for some definite time - P*t=W (measured in J) - so "energy" was correct but maybe misleading. Jan 26, 2014 at 11:15
• For the temperatures above only the T_a and the T_o are meant to be defined by the heating process. The T_b I assumed to be the result that the inner walls cause some form of insulation (hence over time the room will get eventually warmer), while still there is the outer wall with would make it sensible to estimate that the (b) room is warmer than the outer world (as the heat flow is hindered)...... conceptualized with electric-circuit thinking the Temp = the voltage, the heat = curren and the walls are resistors.... Jan 26, 2014 at 12:48

The question is highly hypothetic - but let's tackle it :-)

I am going to look at the total Power (measured in W) needed to maintain 293 K in the living room.

## Premises

• The heat flow through any wall is directly proportional to the Thermal conductivity k (material constant), the area of the wall and the temperature difference and indirectly proportional to the thickness of the wall. (We ignore convection effects for now).
• your assumption of zero heat flow through the side walls (and ceiling, floor which you did not mention) is just that but lets keep it that way for now.

## Calculation

1. Scenario: only the living room is heated

• The main heat flow is through the right wall
• the intermediate room has a higher temperature than the kitchen - so your assumption of 283 K in the kitchen will not hold. I'd assume roughly 287 K in intermediate and 280 K in the kitchen.
• consequence: To maintain the desired temperature you have to replace the (comparatively small) heat flow through the left wall and the (roughly) 3 times greater heat flow through the right wall. That means: you loose less heat through the left wall than you would if it were directly at the outside but more compared to "total insulation" (and only a third of the amount you loose through the right wall).
2. Scenario: you heat the kitchen and maintain 293 K there too

• the intermediate room has only walls to rooms at 293 K - eventually it will get that temperature itself
• so in your living room there will be "no" heat flow through the left wall (remember: you assumed perfectly insulated walls all around it).
• The power needed to maintain 293 K in your living room is now only determined by the flow through the left wall (the same as before) which accounts for about 3/4 of the power needed in scenario 1.
• But you need the same power to maintain 293 K in your kitchen
• Consequence: you need about 75% more power to maintain the desired temperature - and thus more energy through a day (or through the winter).
• thank you. When I can I will try to look into the answer. Good effort thank you. To avoid unnecessary confusion: when you tell "2. Scenario: you heat the kitchen and maintain 393 K there too" you mean 293K, do you? is it that you conclude in 1. that it is an increasing losses to have the not-heated rooms in between, as compared to the Wall on the right? That is even when both outer walls have the same Insulation (i.e. material and thickness)? Jan 26, 2014 at 12:43