2. The heat capacity of one mole of aluminum at low temperature (below 50 K) follows...

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 from the free electrons and the second term is due to lattice vibrations.) Use this expression to derive a formula for the molar entropy of aluminum as a function of temperature, assuming that the entropy at 0 K is zero. Finally, determine the ratio of the multiplicity 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 hot water at 55 ◦C with 25 liters of cold water at 10 ◦C. Assume that the tub is insulated fiberglass that thermally isolates the water. You can also assume that the mixing happens quickly enough that energy is not lost to the air through the open surface of the water.

(a) How much heat is involved in warming the water?

(b) How much entropy did you create?

Expert Solution

genius_generous answered 1 year ago

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