Resistance of a wire at 0° C, 100° C and t° C is found to be 10 Ω, 10.2 Ω and 10.95 Ω respectively. The temperature t in Kelvin scale is _________.

Solution

Physics sir · 4 steps

Use the 0 °C and 100 °C readings to find α, then find t, and add 273 at the end.

1. Linear model. For a metal wire, resistance rises linearly with temperature: Rₜ = R₀(1 + α t), where R₀ is the resistance at 0°C and t is in degrees Celsius.
2. Find alpha. From 0°C to 100°C: 10.2 = 10(1 + 100α). So 100α = 0.02 and α = 2 × 10⁻⁴ °C⁻¹.

   10.95 = 10(1 + 2 × 10⁻⁴ t) ⇒ 2 × 10⁻⁴ t = 0.095

3. Solve for t. t = 0.095/(2 × 10⁻⁴) = 475°C.
4. So. In kelvin, T = 475 + 273 = 748 K. The answer is 748.

The common slip: 475. Stopping at the Celsius value gives 475. The question asks for kelvin, so add 273.

The idea to keep. In Rₜ = R₀(1 + α t), t is a Celsius temperature measured from 0°C. Do all the work in Celsius, and convert to kelvin only if the question asks for it.

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