Step 1: Ratio Analysis.
The ratio \( \frac{E{\lambda}_1 b_2}{E{\lambda}_1 b_1} \), dependent on the temperature ratio \( \frac{T_2}{T_1} \), usually represents a specific heat or thermal conductivity ratio.Step 2: Final Result.
This ratio equals \( \left( \frac{T_2}{T_1} \right)^4 \), based on thermodynamic principles. Final Answer: \[ \boxed{\left( \frac{T_2}{T_1} \right)^4} \]