# At low temperatures, the temperature dependence of the heat capacity has a significant effect on the internal energy. (a) The heat capacity of a non-metallic solid at very low temperatures (close to T = 0) typically varies as aT3, where a is a constant. How does its internal energy vary? (b) Suppose that the molar internal energy of a substance over a limited temperature range can be expressed as a polynomial in T as Um(T) = a+ bT + cT2. Find an expression for the constantvolume molar heat capacity at a temperature T.

At low temperatures, the temperature dependence of the heat capacity has a significant effect on the internal energy. (a) The heat capacity of a non-metallic solid at very low temperatures (close to T = 0) typically varies as aT3, where a is a constant. How does its internal energy vary? (b) Suppose that the molar internal energy of a substance over a limited temperature range can be expressed as a polynomial in T as Um(T) = a+ bT + cT2. Find an expression for the constantvolume molar heat capacity at a temperature T.

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