In Lecture I described many ways by which the constant pressure specific heat capacity of water an other substances could be determined as a function of temperature. Here we will go through this exercise for Cu for temperatures ranging from 25°C to 1000°C. At 25°C and 1 atm pressure, the density of Cu is 8.96 g/cm³. Its molar mass is 63.546 g/mol. For the purposes of this problem, you can assume the specific volume of water is exactly 1.00 mL/g* at 25°C and 1 atm and that CP,H₂O is constant and equal to 1.00 cal/g/K. (a) Suppose you machine a block of Cu so that it measures exactly 1 cm x1 cm x1 cm at 25°C and 1 atm pressure. You then heat the block to 100°C and submerge it in a 100 mL water bath that is initially at 25.000°C. The final temperature of the water and Cu at equilibrium is 25.624°C. Determine the average value of CP.cu over the temperature range 25.624°C to 100°C in cal/g/K. (answer: 0.093636 callg/K) (b) Now suppose you conduct the same experiment described in (a), except the Cu block is initially at 200°C when submerged in the 25.000°C water, and the final equilibrium temperature is 26.480°C. Determine the average value of CP.Cu over the temperature range 100°C to 200°C in cal/g/K. (answer: 0.096337 callg/K) (c) Now suppose you continue these experiments, each time making the initial Cu temperature 100°C higher, and record the following final equilibrium temperatures. Determine the average value of Cp,Cu for each 100°C interval. You may wish to setup a spreadsheet for these calculations since you will need to use all the preceding values of CP,cu for each interval. (answer: 0.117158 callg/K for the 900°C to 1000°C interval) Initial Cu Temperature Final Equilibrium Temp. 27.353°C 28.238°C 29.136°C 30.053°C 30.992°C 300°C 400°C 500°C 600°C 700°C 800°C 900°C 1000°C 31.960°C 32.961°C 34.002°C (d) Suppose you assumed Cp.cu was constant at the value determined in part (a) and used it to compute the amount of heat required to raise the temperature of a fixed amount of Cu from 25°C to 1000°C at a constant pressure of 1 atm. By what percent would your result be off compared to that if you accounted for the temperature dependence of Cp,cu? (answer: It would be underestimated by 9.89%)