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At low temperatures the specific heat of a metal varies as S = a T³, with a constant and T the absolute temperature. How much heat is required to raise the temperature of unit mass of the metal from T = 1 K to T = 2 K?

1. 3 a
2. 15a/4
3. 2a/3
4. 12a/5

Correct answer: 15a/4

Solution

Integrating a T³ from 1 to 2 gives a(16 - 1)/4 = 15a/4.

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