Surface X has a temperature T_X and emissivity ε_x. Surface Y has a temperature T_Y and emissivity ε_y. The two surfaces emit radiation at the same rate.

What is the ratio \(\frac{{{T_{\rm{X}}}}}{{{T_{\rm{Y}}}}}\)?

A. \({\left( {\frac{{{\varepsilon _{\rm{y}}}}}{{{\varepsilon _{\rm{x}}}}}} \right)^{\frac{1}{4}}}\)

B. \({\left( {\frac{{{\varepsilon _{\rm{x}}}}}{{{\varepsilon _{\rm{y}}}}}} \right)^{\frac{1}{4}}}\)

C. \({\left( {\frac{{{\varepsilon _{\rm{y}}}}}{{{\varepsilon _{\rm{x}}}}}} \right)^4}\)

D. \({\left( {\frac{{{\varepsilon _{\rm{x}}}}}{{{\varepsilon _{\rm{y}}}}}} \right)^4}\)