2. The heat capacity of one mole of aluminum at low temperature(below 50 K) follows the form
CV = aT+bT3
where a = 0.00135 J/K2 and b =2.48×10-5 J/K4. (The first term comes fromthe free electrons and the second term is due to latticevibrations.) Use this expression to derive a formula for the molarentropy of aluminum as a function of temperature, assuming that theentropy at 0 K is zero. Finally, determine the ratio of themultiplicity of a mole of aluminum at 10 K to its value at 1 K.
3. In order to take a nice warm bath, you mix 50 liters of hotwater at 55 â—¦C with 25 liters of cold water at 10 â—¦C. Assume thatthe tub is insulated fiberglass that thermally isolates the water.You can also assume that the mixing happens quickly enough thatenergy is not lost to the air through the open surface of thewater.
(a) How much heat is involved in warming the water?
(b) How much entropy did you create?
