Consider a metal in which electrons are well described in terms of independent electrons moving in a periodic potential. There is only one energy band which crosses the fermi energy. For the purpose, it suffices to consider this energy band, put the fermi energy in the middle of this band, disregard all others. Imagine that we can vary that width of this band without changing other parameters. Would the electronic specific heat increase or decrease as the bandwidth is increased?
Write down the arugments explicitly please. (Qualitative physical argument would be enough)