Answer
$574.6 \mathrm{K}$
Work Step by Step
Conversion formulas:
$\left[\begin{array}{ll}
T_{\mathrm{F}}=\frac{9}{5}T_{\mathrm{C}}+32 & 16-1\\
T_{\mathrm{C}}=\frac{5}{9}(T_{\mathrm{F}}-32) & 16-2\\
T=T_{\mathrm{C}}+273.15 & 16-3
\end{array}\right]$
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$T=T_{\mathrm{C}}+273.15$
substitute $T_{C}$ using 16-2
$T=\displaystyle \frac{5}{9}(T_{\mathrm{F}}-32)+273.15$
... we want $T=T_{F},$
$T=\displaystyle \frac{5}{9}(T-32)+273.15$
$T=\displaystyle \frac{5}{9}T-\frac{160}{9}+273.15$
$\displaystyle \frac{4}{9}T=273.15-\frac{160}{9}$
$T=\displaystyle \frac{9}{4}(273.15-\frac{160}{9})=574.6 \mathrm{K}$
