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

Solution

Physics sir · 3 steps

Resistance rises 2 Ω per 100°C, so add four such rises to 8 Ω.

1. Linear scale. A platinum resistance thermometer assumes that resistance changes linearly with temperature. The ice point (0°C) and the steam point (100°C) fix the two ends of the scale.

   t = (Rₜ - R₀)/(R₁₀₀ - R₀) × 100°C

2. Put in numbers. With R₀ = 8 Ω, R₁₀₀ = 10 Ω and t = 400°C: 400 = (Rₜ - 8)/2 × 100. This gives Rₜ - 8 = 8.
3. So. Rₜ = 16 Ω, which is option (b).

The idea to keep. For any linear thermometer, the reading's share of the fundamental interval equals the temperature's share of 100°C. Set up that ratio and solve.

Answer from the NTA final answer key. Solution by PrepWiser.