1. Use the linear relation for a platinum resistance thermometer

For a platinum resistance thermometer, resistance varies approximately linearly with temperature:

$R_t = R_0(1 + \alpha t)$

where:

• $R_0$ = resistance at $0^\circ C$
• $R_t$ = resistance at temperature $t$

2. Given data

At ice point $(0^\circ C)$: $R_0 = 8\,\Omega$

At steam point $(100^\circ C)$: $R_{100} = 10\,\Omega$

So,

$10 = 8(1 + 100\alpha)$

3. Find $\alpha$

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

$1.25 = 1 + 100\alpha$

$100\alpha = 0.25$

$\alpha = 0.0025\,^\circ C^{-1}$

4. Find resistance at $400^\circ C$

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

$R_{400} = 8(1 + 1)$

$R_{400} = 8 \times 2 = 16\,\Omega$

5. Check options

• A: $10\,\Omega$ ❌
• B: $16\,\Omega$ ✅
• C: $8\,\Omega$ ❌
• D: $2\,\Omega$ ❌

Therefore, the correct answer is B.