A metal bar in a low temperature physics experiment with mass m$=92$kg had its temperature raised from T$1=28$K to T$2=41$K $.$ The metal bar has a specific heat that is a function of temperature: c$($T$)=$A$+$T where A$=440$J$/($kg$$K$)$ and $=11$J$/($kg$$K$2).$ Note the metal bar does not change in volume as it is heated.Calculate the amount of heat in joules required to raise the temperature on the metal bar as stated. Calculate the change in heat, in units of joules, of the metal bar when cooling from T$2$ to T$1$ without any change in volume. Write an approximation of c$($T$)$ for the metal rod at very high temperatures $($say T$>>1000$K $).$ c$($T