Question

Resistance is 6 ohm at heat scale 0°C, resisitance at 100°C is 7 ohm. If the value of resistance is 8 ohm at unknown temperature, count the unknown temperature. ​

Answer 1

Answer: The required temperature is 200°c.

Explanation:

We know that

Rt=Ro+α(T2-T1)

=> Rt-Ro=α(T2-T1)

Rt-Ro is directly proportional to T2-T1.

From given question Let Ro=6ohm,Rt1=7ohm Rt2=8ohm, To=0°c, T1=100°c

,T2=x°c

From the above data

(Rt2-Ro)/(Rt1-Ro)=

(T2-To)/(T1-To)

Therefore

(8-6)/(7-6)=(x-0)/(100-0)

2/1=x/100

x=200°c

Therefore the temperature at 8ohm will be 200°c.

Answer 2

Let R' be the resistance at any temperature (in Kelvin),

R° be the resistance at 0°C or 273.15 K

∆T be the temperature difference from 0°C and

K be temperature coefficient of resistance change.

We have R° = 6 ohms

R' = R°(1 + K∆T)

at 100°C or 373.15 Kelvin...

7 = 6(1 + K(100))

100K = 7/6 - 1

K = 1/600 per Kelvin

for temperature at 8 ohms...

8 = 6(1 + 1/600∆T)

1/600∆T = 8/6 - 1

∆T = 2/6 x 600

∆T = 200 Kelvin

T - 273.15 = 200

T = 473.15 Kelvin = 200°C

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