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The temperature T may be expressed as the rate of energy increase per unit increase in the state uncertainty under no-work conditions. The consequences of such a choice for heat capacities are explored. I show that the ratio of the total thermal energy E to kT is the multiplicity exponent (log–log derivative of the multiplicity) with respect to energy, as well as the number of base-b units of mutual information that is lost about the state of the system per b-fold increase in the thermal energy. Similarly, the no-work heat capacity C_V is the multiplicity exponent for temperature, making C_V independent of the choice of the intensive parameter associated with energy (for example, kT vs 1/kT) to within a constant, and explaining why its usefulness may go beyond the detection of thermodynamic phase changes and quadratic modes. ©2003 American Association of Physics Teachers.