27 Consider a twodimensional ideal gas of N non-relativistic spinless fermions of mass m in a box of area A. (a) Find the density of single-particle states g() at energy a. (b) Write the equation that determines the chemical potential p of the gas at temperature T. Show that in the limit when the fugacity C E e|3IJ 4-: 1 (classical limit), the approximate solution to this equation is N ka C m E where Nc = A2??? . (Hint: in the limit can we have em\") ) >> 1 for any a 2 0.)