Insulation helps to keep heat inside a house, meaning as less heats escapes there is no need to heat the house up, normally by Central Heating, therefore saving energy.
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it depends on the r-value of the insulation and the area or temperature range of the climate it is to be installed
Technically, no. However, in this context, yes. It wouldn't actually save energy, but it can lower the amount if energy needed to do a task. For example, if you insulate your house well, you would not need to heat/cool is as aggressively because the hot/cold air would not pass through the walls to the outside air nearly as easily as a house that has no or poor insulation.
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The critical radius of insulation is a counterintuitive concept within the study of heat transfer.
it is a good thing i think R Value is the thermal resistance of a given material. The higher the R Value the more thermal resistance and the better the insulation. So, an R48 roof system is warmer than an R32 roof system. All insulation materials are rated by their R Value. An inch of rigid insulation has a higher R Value than an inch of fiberglass insulation. Check with the insulation manufacturer for the R Value.