Answer
$T_C^{\circ}=73-273=-200C^{\circ}$
Work Step by Step
$v_{rms}=\sqrt\frac{3RT}{M}$......eq(1)
The value of $v_{rms}$ was found from part (a) to be 511 m/s. Therefore, half $v_{rms}=\frac{511}{2}=255.5 \frac{m}{s}$
We now rearrange eq (1) to make $T$ the subject of the formula:
$T=\frac{(v_{rms})^2(M)}{3R}$
Substituting the values into this equation to solve for $T$:
$T=\frac{(255.5)^2(28\times10^{-3})}{3(8.314)}=73 K$
Therefore, $T_C^{\circ}=73-273=-200C^{\circ}$
