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

Question

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.

Answer 1

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).