practice, this can be established experimentally for a given system. 1 Equipartition equations Equipartition says that U = NDOF NkT + const. (4) 2 Spring 2024 This applies in equilibrium, so this counts for all points during a quasi-static process, assuming equipartition applies. You must generally be told or find out that equipartition applies to a given situation, by measuring the heat capacity. Efficiency Heat engines are made up of closed thermodynamic paths. Since the path is closed, the change in total entropy is Stot 0. Setting this to zero (the minimum) results in the Carnot efficiency: carnot = W 1 TC , (5) QH TH where QH is the amount of heat taken from a hot reservoir, and W is the amount of work done. It is very useful to draw an engine diagram to understand the energy flow! 2 1 Cycles Nitrogen gas with translational and rotational degrees of freedom starts at TA = 300 K, pA = 1 atm, and a volume of VA = 1 liter. (state (A)). You may treat it as an ideal gas. 1. Starting at state (A), the gas is expanded adiabatically to VB = 2 liters, state (B). 2. Starting at state (B), the gas is isothermally compressed to VC = 1 liter, state (C). 3. Starting at state (C), the gas is heated at constant volume back to state (A). The relationship between p and V for an ideal gas with equipartition is Isothermal: piVi = pf Vf = constisothermal Adiabatic: piV = pf V = constadiabat, where = NDOF +2 if NDOF Isochoric (constant volume): Vi = Vf . 1.1 Qualitative analysis For each of the three processes, describe which thermodynamic quantities (p,V,T,U,S) don't change, which do change, and how they change. Also, describe if the system does positive or negative work and if heat flows in or out of the system. Briefly explain your reasoning. 1. (A) (B) 2. (B)(C)