Chapter 8, Problem 36P

Mechanical engineers, as well as most other engineers, use thermodynamics extensively in their work. The following polynomial can be used to relate the zero-pressure specific heat of dry air, $c_p\text{kJ}/\left(\text{kg}\text{K}\right)$, to temperature $\left(\text{K}\right)$:

$\begin{array}{l}{c}_p=0.99403+1.671\times {10}^{-4}T+9.7215\times {10}^{-8}{T}^2\\ -9.5838\times {10}^{-11}{T}^3+1.9520\times {10}^{-14}{T}^4\end{array}$

Determine the temperature that corresponds to a specific heat of $1.2\text{kJ}/\left(\text{kg}\text{K}\right)$.