OpenStax College Physics for AP® Courses, Chapter 15, Problem 50 (Problems & Exercises)

This is College Physics Answers with Shaun Dychko. 1.60 times 10 to the 5 joules of heat are transferred into a meat pie which is initially at a temperature T 1 of 20.0 degrees Celsius which we convert into Kelvin by adding 273.15; the change in entropy of the meat pie, we are told, is 480 joules per Kelvin and the question is what is the meat pie's final temperature? So change in entropy is the heat absorbed by a system divided by its temperature and for small temperature changes, we can take this T to be the average of the two temperatures. So T 2 is what we are trying to find here so T is gonna be T 1 plus T 2 over 2. Now dividing by this fraction is the same as multiplying by its reciprocal so that's what I prefer to do instead of having a fraction divided by a fraction, multiply by the reciprocal of this fraction. So that means ΔS equals Q times 2 over T 1 plus T 2 and now we do a bunch of algebra to solve for T 2. So we'll multiply both sides by T 1 plus T 2 in which case, we have T 1 plus T 2 times ΔS equals 2Q and then distribute the ΔS into the brackets here we get T 1ΔS plus T 2ΔS equals 2Q and then subtract T 1ΔS from both sides and then you get T 2ΔS equals 2Q minus T 1ΔS then divide both sides by the change in entropy and then we have solved for T 2. So T 2 is 2 times the heat transferred into the meat pie minus the initial temperature times the change in entropy all divided by the change in entropy. So that's 2 times 1.60 times 10 to the 5 joules minus 293.15 Kelvin times 480 joules per Kelvin all divided by 480 joules per Kelvin which is 373.517 Kelvin and we subtract 273.15 to convert that into degrees Celsius and that is exactly 1.00 times 10 to the 2 degrees Celsius.