Answer
$9.59\frac{W}{K}$
Work Step by Step
We know that
Rate of change of entropy inside house is given as
$dS=\frac{dQ}{dT}$
We plug in the known values to obtain:
$dS=\frac{-20KJ}{295}=-67.78\frac{J}{K}$
Similarly, Rate of change of entropy outside house is given as
$dS=\frac{dQ}{dT}$
We plug in the known values to obtain:
$dS=\frac{20KJ}{258.5}=77.37\frac{J}{K}$
Now the total change in entropy$= 77.37-67.78=9.59\frac{J}{K}$
and the rate of change of entropy is $\frac{9.59\frac{J}{K}}{s}=9.59\frac{W}{K}$
