Answer
$T_C^{\circ}=899C^{\circ}$
Work Step by Step
We know that
$v_{rms}=\sqrt\frac{3RT}{M}$..............eq(1)
Since $v_{rms}$ was found to be 511 in part (a), Twice the $v_{rms}$ is equal to $2\times511=1022\frac{m}{s}$
We re-arrange eq(1) to:
$T=\frac{(v_{rms})^2(M)}{3R}$
Now we substitute the values in this equation to solve for $T$:
$T=\frac{(1022)^2(28\times10^{-3})}{3(8.314)}=1172K$
$T_C^{\circ}=1172-273=899C^{\circ}$
$T_C^{\circ}=899C^{\circ}$
