Question

The resistance of a coil used in a platinum resistance thermometer at 0°C is 3.00 ohm and at 100 °C is 3.75 ohm, its resistance at unknown temperature is measured at 3.15 ohm. Calculate the unknown temperature.
Hint: answer = 1127 K
Please write the complete and correct solution.
Irrelevant answer will be reported. ​

Answer 1

Given:

Resistance of a coil used in a platinum resistance thermometer at 0°C is 3.00 ohm and at 100 °C is 3.75 ohm, its resistance at unknown temperature is measured at 3.15 ohm.

To find:

Unknown temperature.

Calculation:

Let unknown temperature be x K.

In the 1st case:

$R1 = R(1 + \alpha \Delta \theta)$

$= > 3.75 = 3 \{1 + \alpha (373 - 273) \}$

$= > 3.75 = 3 \{1 + 100 \alpha \}$

$= > 1 + 100 \alpha = \dfrac{3.75}{3}$

$= > 1 + 100 \alpha = 1.25$

$= > 100 \alpha = 0.25$

$= > \alpha = 25 \times {10}^{ - 4}$

In the 2nd case:

$R2 = R(1 + \alpha \Delta \theta)$

$= > 3.15= 3 \{1 + \alpha (x - 273) \}$

$= >1 + \alpha (x - 273) = \dfrac{3.15}{3}$

$= >1 + \alpha (x - 273) = 1.05$

$= >\alpha (x - 273) = 0.05$

$= >25 \times {10}^{ - 4} \times (x - 273) = 0.05$

$= > (x - 273) = \dfrac{ 0.05}{25 \times {10}^{ - 4} }$

$= > (x - 273) = \dfrac{100}{5}$

$= > (x - 273) = 20$

$= > x = 293 \: K$

So, final answer is:

$\boxed{ \red{ \bold{ \large{ x = 293 \: K }}}}$

Answer 2

$\huge\underbrace\orange{Answer:-}$

Please refer to the given attachment...