Filters come in many varieties.  In another lesson you should have learned about an electrical filter.  In that filter the input was a voltage and the output was also a voltage.  When you computed the ratio of output to input the ratio was dimensionless.  You might have assumed that all filters were like that.  In this note we want you to consider another kind of filter that you might have experienced.

        Consider the amount of solar radiation received in Pennsylvania, for example, over the course of a year.  The maximum solar radiation occurs on June 21 or thereabouts, and the minimum around December 20.  However, the minimum temperature occurs on February 2, and the maximum temperature sometime early in August.  That's shown in the sketch below.  The minimum in central Pennsylvania is somewhere around 35^oF, and the maximum is around 75^oF.

        The reason for this behavior is that there is a thermal time constant in the system.  That thermal time constant produces a lag in the response of the system to incident solar radiation.  The radiation curve is approximately sinusoidal.

        There is a question buried in here for you.

        What would the maximum and minimum temperature be without the filtering effect?  You will need to think using what you know about filters to estimate the max and min temperatures for this problem.