Part $($a$)$ of the drawing shows a rectangular bar whose dimensions are $L_{0}2L_{0}3L_0.$ The bar is at the same constant temperature as the room $($not shown$)$ in which it is located. The bar is then cut, lengthwise, into two identical pieces, as shown in part $($b$)$ of the drawing. The temperature of each piece is the same as that of the original bar.

$($a$)$ What is the ratio of the power absorbed by the two bars in part $($b$)$ of the drawing to the single bar in part $($a$)?$

$($b$)$ Suppose that the temperature of the single bar in part $($a$)$ is $425$ K $.$ What would the temperature $($in kelvins$)$ of the room and the two bars in part $($b$)$ have to be so that the two bars absorb the same power as the single bar in part $($a$)?$