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 :

The correct answer is 16 ��.

A platinum resistance thermometer works on the principle that the electrical resistance of platinum changes linearly with temperature. The relationship is given by:

R_T=R_0(1+\alpha T)

where RT is the resistance at temperature T, R0 is the resistance at 0°C (ice point), and α is the temperature coefficient of resistance of platinum.

Step 1: Identify the known values from the problem.

- Resistance at ice point (T = 0°C): R0 = 8 Ω
- Resistance at steam point (T = 100°C): R100 = 10 Ω
- Temperature of hot bath: T = 400°C

Step 2: Find the temperature coefficient of resistance (α).

Applying the formula at the steam point (T = 100°C):

R_{100}=R_0(1+\alpha \times 100)

10=8(1+100\alpha )

\frac{10}{8}=1+100\alpha

1.25=1+100\alpha

100\alpha =0.25

\alpha =0.0025\text{per °C}

Step 3: Calculate the resistance at 400°C.

Now applying the formula for T = 400°C:

R_{400}=R_0(1+\alpha \times 400)

R_{400}=8(1+0.0025\times 400)

R_{400}=8(1+1)

R_{400}=8\times 2

R_{400}=16\text{Ω}

Conclusion: When the platinum wire is inserted into the hot bath at 400°C, its resistance becomes 16 Ω.

Intuitively, from 0°C to 100°C the resistance increased by 2 Ω (from 8 Ω to 10 Ω), meaning the resistance increases by 0.02 Ω per °C. Over 400°C, the total increase would be 0.02 × 400 = 8 Ω, giving a final resistance of 8 + 8 = 16 Ω. ✓