Metal bar temperature when kinetic energy is multiplied by 9.49

[NasuSama]

Homework Statement

bar of metal is at temperature T1 = 678 °C. Suppose the average kinetic energy of the molecules in the metal is multiplied by constant a = 9.49. Find T2, the new Celsius temperature.

Homework Equations

$KE_{avg} = 3/2 kT$

The Attempt at a Solution

I worked out this way:

$KE_{avg} = 3/2 kT_{1}$
$aKE_{avg} = 3a/2 kT_{1}$
$3a/2 kT_{1} = 3/2 kT_{2}$
$aT_{1} = T_{2}$
$9.49 * (678 + 273) - 273 = T_{2}$

 

[NasuSama]

Is it correct, or did I do something wrong?

 

[haruspex]

Looks right to me.

 

[rude man]

Is it correct, or did I do something wrong?

right.