We have N distinguishable particles. Each particle from(1 to N) can adopt a countably infinite number of microstates (ia) that can be labelled ia=0,1,2,3...... with corresponding energies Ea(ia)=ia. ( eg. 0th microstate has energy 0, the 1th microstate has energy 1 the 2nd microstate has energy 2 so on..) If particle 1 has microstate i1, particle 2 has microstate i2,...., the the energy of N particle system is the sum of independent particles E=sum of ia. Determine the microcanonical partition function, omega. Determine fundamental relation of system, using Stirling's approximation Determine the energy and heat capacity for the system as a function of temperature using Stirling's approximation. Determine a fundamental relation for the Helmholtz potential of the system