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- ans= 1127K)
please write the correct solution.
irrelevant answers will be reported.
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Answer 1

Given : The resistance of a coil used in a platinum resistance thermometer at 0°C is 3Ω and at 100°C is 3.75Ω, it resistance at unknown temperature is measured at 3.15 Ω.

To find : The unknown temperature.

solution : using formula, R' = R[1 + α∆T)]

at 0°C , $R_0$ = 3Ω

at 100°C , $R_{100}$ = 3.75 Ω

and at T°C , $R_T$ = 3.15 Ω

case 1 : $R_{100}=R_0(1+\alpha\Delta T)$

⇒3.75 = 3[1 + α(100 - 0)]

⇒0.75 = 300α

⇒α = 0.75/300 = 0.25/100 = 2.5 × 10¯³ /°C

case 2 : $R_T=R_0(1+\alpha T)$

⇒3.15 = 3[1 + 2.5 × 10¯³ × T ]

⇒3.15 = 3 + 7.5 × 10¯³ T

⇒T = 0.15/(7.5 × 10¯³) = 150/7.5 = 20 °C

therefore unknown temperature in Kelvin is 20+ 273 = 293K

Answer 2

Answer:

the answer is 1127K....