The constant-volume heat capacity is proportional to the variance in this quantity. Euler’s equation for this quantity takes advantage of the fact that it is homogenous in each of its three arguments. (-5[1])For an ideal gas, this quantity’s constant hypersurface in momentum space is a spherical shell. The partial derivative of entropy with respect to this quantity is (15[1])the inverse temperature. (15[1])In the Boltzmann distribution, (15[1])a state’s probability (-5[1])is proportional to “e to the negative (*) beta times this quantity,” (-5[2])which is fixed in the microcanonical ensemble. (-5[1])Since its (10[1])natural variables (10[1])are S and (10[1])V, performing two (10[1])Legendre (“leh-JOND”) transforms on this quantity gives (-5[1])Gibbs free energy. (-5[1])The change in this quantity (10[1]-5[1])symbolized (10[1])U (10[1])is equal (10[3]-5[1])to (10[1]-5[2])heat (10[1])plus work. (10[3]-5[1])For (10[2]-5[1])10 (10[1])points, the first (10[1])law (-5[1])of thermodynamics is equivalent to the (-5[1])conservation of what quantity? ■END■ (10[8])