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Question:

Using equipartition of energy, the specific heat (in J/kgK) of aluminium at high temperature can be estimated to be (atomic weight of aluminium=27)

923

25

1850

410

Solution:

The theorem of equipartition of energy states that molecules in thermal equilibrium have the same average energy associated with each independent degree of freedom of their motion and that the energy is 1/2kT per molecule where k is Boltzmann constant. For n moles, K.E.=1/2nRT where R is gas constant. An atom in a solid state has no degrees of freedom for translational and rotational motion. At high temperatures, due to vibration along 3 axes it has 3 X 2(directions) = 6 degrees of freedom. F = 6 due to vibration at high temperature. U=6(1/2)RT.. (I) Heat capacity can be obtained by differentiating equation (I) C=dU/dT=3R=24.94J/molK for specific heat capacity the quantity can be divided by aluminium molecular mass specific heat capacity=24.94/27 gm/mole=923J/kgK Hence, correct answer is option A