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It's a matter of a space being able to 'breathe'. While increasing insulation will reduce heat gain to a space it will also reduce heat loss to a space.

Say your system is a space with exterior ceiling, floors, and walls, and typical office internal loads. During unoccupied hours when the sun is down Q_in is probably pretty small and less than Q_out with a roof insulation of say R-30, so your space will cool. Now when that's increased to R-34 we'll assume that both Q_in and Q_out are reduced by 5%, and since Q_in was smaller than Q_out dQ_in < dQ_out, so the space will cool less than the previous situation. Where this becomes tricky is when you've increased your insulation to a point where you're now trapping all the heat from your internal loads inside the space such that it can't escape at night when it was previously able to.

In other news MathJAX (i.e. $\Delta$) isn't working.

It's a matter of a space being able to 'breathe'. While increasing insulation will reduce heat gain to a space it will also reduce heat loss to a space.

Say your system is a space with exterior ceiling, floors, and walls, and typical office internal loads. During unoccupied hours when the sun is down Q_in $Q_in$ is probably pretty small and less than Q_out $Q_out$ with a roof insulation of say R-30, so your space will cool. Now when that's increased to R-34 we'll assume that both Q_in $Q_in$ and Q_out $Q_out$ are reduced by 5%, and since Q_in $Q_in$ was smaller than Q_out dQ_in $Q_out$ $\Delta Q_in$ < dQ_out, $\Delta Q_out$, so the space will cool less than the previous situation. Where this becomes tricky is when you've increased your insulation to a point where you're now trapping all the heat from your internal loads inside the space such that it can't escape at night when it was previously able to.

In other news MathJAX (i.e. $\Delta$) isn't working.

It's a matter of a space being able to 'breathe'. While increasing insulation will reduce heat gain to a space it will also reduce heat loss to a space.

Say your system is a space with exterior ceiling, floors, and walls, and typical office internal loads. During unoccupied hours when the sun is down $Q_in$ $Q_{in}$ is probably pretty small and less than $Q_out$ $Q_{out}$ with a roof insulation of say R-30, so your space will cool. Now when that's increased to R-34 we'll assume that both $Q_in$ $Q_{in}$ and $Q_out$ $Q_{out}$ are reduced by 5%, and since $Q_in$ $Q_{in}$ was smaller than $Q_out$ $Q_{out}$ $\Delta Q_in$ Q_{in}$ < $\Delta Q_out$, Q_{out}$, so the space will cool less than the previous situation. Where this becomes tricky is when you've increased your insulation to a point where you're now trapping all the heat from your internal loads inside the space such that it can't escape at night when it was previously able to.