A hot-air balloon has a durable fabric envelope of constant volume \(V_0\) with an opening at the bottom, ensuring that the pressure inside the balloon always matches the surrounding atmospheric pressure \(P_0\). The ambient air outside has a constant temperature \(T_{\text{ext}}\) and constant density. The air inside the balloon, initially at temperature \(T_1 = 300\text{ K}\), is heated by a burner to a uniform temperature \(T_2 = 400\text{ K}\). What is the ratio \(F_{B,2} / F_{B,1}\) of the buoyant force exerted on the balloon at \(T_2\) to the buoyant force exerted on the balloon at \(T_1\)?