35. Consider a simple thermodynamic system in which par- ticles can occupy only two states: a lower state, whose energy we define as 0, and an upper state, energy E (a) Carry out the sum (with only two states, integration is certainly not valid) giving the average particle energy E, and plot your result as a function of temperature. (b) Explain qualitatively why it should behave as it does. (c) This system can be used as a model of paramagne- tism, where individual atoms' magnetic moments can either be aligned or antialigned with an external mag- netic field, giving a low or high energy, respectively. Describe how the average alignment or antialignment depends on temperature. Does it make sense?