Question

A platinum resistance thermometer reads 0° when its resistance is 80 Ω and 100° when its resistance is 90 Ω.
Find the temperature at the platinum scale at which the resistance is 86 Ω.

Answer 1

$\Large\underline{\underline{\sf \green{Given}:}}$

• A platinum resistance thermometer reads 0° when its resistance is 80 Ω

• and 100° when its resistance is 90 Ω

$\Large\underline{\underline{\sf \green{To\:Find}:}}$

• Find the temperature at the platinum scale at which the resistance is 86 Ω.

$\Large\underline{\underline{\sf \green{Formula\:Used}:}}$

$\large{\boxed{\sf \red{T=\dfrac{R_t-R_0}{R_{100}-R_0} ×100}}}$

Here ,

$\sf{R_t}$ = Resistance at which temperature is to be measured.

$\sf{R_0}$ = Resistance at 0°C

$\sf{R_{100}}$ = Resistance at 100°C

$\Large\underline{\underline{\sf \green{Solution}:}}$

By substituting Value

$\implies{\sf T=\dfrac{86-80}{90}×100 }$

$\implies{\sf T=\dfrac{6}{10}×100}$

$\implies{\sf T=60°C}$

$\Large\underline{\underline{\sf \green{Answer}:}}$

•°• 60°C is the temperature at the platinum scale at which the resistance is 86 Ω.

Answer 2

The temperature at the platinum scale at which the resistance is 86 Ω is $t=60^{\circ} \mathrm{C}$.

Explanation:

Step 1:

Given,

Let resistance at $\mathrm{O}^{0}$ temperature is represented by $R_{0}$

Resistance at 1000  temperature is represented as $\mathrm{R}_{100}$

Resistance at t temperature is represented as $R_{t}$

                                $\mathrm{R}_{0}=80 \Omega$

                                $\mathrm{R}_{100}=90 \Omega$

                                $R_{t}=$$86 \Omega$

Step 2:

By using the formula  

                               $t=\frac{R_{t}-R_{0}}{R_{100}-R_{0}} \times 100$  

                               $t=\frac{86-80}{90-80} \times 100$

                               $t=\frac{6}{10} \times 100$

                               $t=60^{\circ} \mathrm{C}$

So the temperature of platinum scale is $60^{\circ} \mathrm{C}$ at $86 \Omega$