(a) Explanation The average energy of each atom is 1 2 k B T . In a pure metallic element, one atom is equal to the one molecule. Write the expression of the total energy of the metallic element. E = 1 2 m v x 2 + 1 2 m v y 2 + 1 2 m v z 2 + 1 2 k x x 2 + 1 2 k y y 2 + 1 2 k z z 2 (1) Here, m is the mass of the molecule. v x is the velocity component in x direction. v y is the velocity component in y direction. v z is the velocity component in z direction. k x is the spring constant in x direction. k y is the spring constant in y direction. k z is the spring constant in z direction. For each degree of freedom, the average energy is 1 2 k B T . Substitute 1 2 k B T for 1 2 m v x 2 , 1 2 k B T for 1 2 m v y 2 , 1 2 k B T for 1 2 m v z 2 , 1 2 k B T for 1 2 k x x 2 , 1 2 k B T for 1 2 k y y 2 and 1 2 k B T for 1 2 k z z 2 in equation (1) (b) To determine The specific heat c of iron and compare the value listed in Table 19.1 . (c) To determine The specific heat c of gold and compare the value listed in Table 19.1 .

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Chapter 21, Problem 21.50AP

(a)

To determine

To show: The molar specific heat of the solid is 3R.

(b)

To determine

The specific heat c of iron and compare the value listed in Table 19.1.

(c)

To determine

The specific heat c of gold and compare the value listed in Table 19.1.

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Chapter 21, Problem 21.49AP

Chapter 21, Problem 21.51AP

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The molar specific heat of the solid is 3 R .

Solution Summary: The author explains how the molar specific heat of the solid is 3R.

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To show: The molar specific heat of the solid is 3R.

The specific heat c of iron and compare the value listed in Table 19.1.

The specific heat c of gold and compare the value listed in Table 19.1.

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Chapter 21 Solutions