What is the temperature inside an ideal refrigerator-freezer that operates with a COP = 7.0 in a $22 ^\circ \textrm{C}$ room?

VIDEO TRANSCRIPT

This is Giancoli answers with Mr. Dychko. The ideal coefficient of performance is the low temperature inside the ideal refrigerator freezer divided by the high temperature outside the freezer minus the low temperature inside. So we'll multiply both sides by this denominator. Our goal is to solve for TL by the way. And it takes a bit of work because it shows up in two places. So we'll multiply both sides by TH minus TL and we get TH minus TL times coefficient of performance in the left equals T L on the right side. And then distribute this coefficient of performance into the brackets. So, we have TH times COP minus TL times COP equals TL and then bring the TL terms together on the same side of the equation by moving this to the right which makes it positive and then switch sides around and then we have TL times COP plus TL equals TH times COP and factor out the low temperature. So, we have low temperature times coefficient of performance plus one equals TH times the COP. Then divide both sides by this bracket and we've solved for TL the temperature inside, the low temperature. So it's going to be the high temperature times the coefficient of performance times one plus the coefficient of performance. So that's 22 degrees Celsius plus 273 to convert it into Kelvin times seven divided by seven plus one makes 258.125 Kelvin and take away 273 to convert it into degrees Celsius and that gives minus 15 degrees Celsius for the temperature inside.