Question

Calculate the energy (in Joules) required to raise the temperature of 1 mole of aluminium from a) T = 0K to T = 10K and b) T = 0K to T = 300K. Calculate these quantities using both the Dulong-Petit classical specific heat i.e. cV = 3R and the quantum mechanical expressions you derived using the Debye approximation above and compare the results. The Debye temperature of Al is 428K. State any approximations made i.e. low temperature limit/high temperature limit etc. It may be necessary to use a computer to calculate some of the integrals.

          Calculate the energy (in Joules) required to raise the temperature of 1 mole of aluminium from a) T = 0K to T = 10K and b) T = 0K to T = 300K. Calculate these quantities using both the Dulong-Petit classical specific heat i.e. cV = 3R and the quantum mechanical expressions you derived using the Debye approximation above and compare the results. The Debye temperature of Al is 428K. State any approximations made i.e. low temperature limit/high temperature limit etc. It may be necessary to use a computer to calculate some of the integrals.

Calculate the energy (in Joules) required to raise the temperature of 1 mole of aluminium from a) T = 0K to T = 10K and b) T = 0K to T = 300K. Calculate these quantities using both the Dulong-Petit classical specific heat i.e. cV = 3R and the quantum mechanical expressions you derived using the Debye approximation above and compare the results. The Debye temperature of Al is 428K. State any approximations made i.e. low temperature limit/high temperature limit etc. It may be necessary to use a computer to calculate some of the integrals.

Added by Michael N.

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