The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are 8Ω and 10Ω respectively. After inserting in a hot bath of temperature 400°C, the resistance of platinum wire is:

In a platinum resistance thermometer, the resistance varies linearly with temperature: $$ R_t = R_0(1 + \alpha t) $$. At the ice point (0°C) $$R_0 = 8\,\Omega$$ and at the steam point (100°C) $$R_{100} = 10\,\Omega$$. Substituting these values yields $$10 = 8(1 + 100\alpha) \Rightarrow 1 + 100\alpha = 1.25 \Rightarrow \alpha = 0.0025$$.

For 400°C the resistance is $$R_{400} = 8(1 + 400 \times 0.0025) = 8(1 + 1) = 8 \times 2 = 16\,\Omega$$. Thus, the correct answer is Option 3: 16 Ω.