question_answer

The heat \[(Q)\] supplied to a solid, which is otherwise thermally isolated from its surroundings, is plotted as a function of its absolute temperature, \[\theta \]. It is found that they are related by the equation. \[Q=a\,{{\theta }^{2}}+b\,{{\theta }^{4}}\](a, b are constants). The heat capacity of the solid is given by

A) \[a\frac{{{\theta }^{3}}}{3}+b\frac{{{\theta }^{5}}}{5}\]

B) \[a\theta +b{{\theta }^{3}}\]

C) \[a\frac{\theta }{3}+b\frac{{{\theta }^{3}}}{5}\]

D) \[2a\theta +4b{{\theta }^{3}}\]