A canonical example of an integrating factor is the calculation of an exact differential of this quantity using the reciprocal of temperature. This quantity is the thermodynamic potential of the microcanonical ensemble. (0[1])The ratio between changes in specific forms of this quantity and volume gives the slope of coexistence curves in (0[1])the (0[1])(*) Clapeyron equation. (0[4])The Clausius theorem (0[1])gives that an integral (10[1])of a change (10[1])in this quantity expressed (0[1])as (10[1])“negative delta Q over T” must (10[1])be (10[1])greater than (10[1])or equal to zero. (10[3])A law of this (10[1])quantity (0[1])implies (10[1])that Carnot engines cannot be (10[1])perfectly (10[1]0[1])efficient (10[1])and establishes (0[3])an “arrow of time.” (10[1])For 10 points, (10[1])the second (10[1])law of thermodynamics (10[4])holds that (10[1])what quantity (10[1])always (10[1])increases (10[1])in the (10[1])universe? (10[4])■END■ (10[5])