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The Electrical Resistance in Ohms of a Certain Thermometer Varies with Temperature According to the Approximate Law the Resistance is 101.6 ω at the Triple-point of Water 273.16 K, and 165.5 Ohm at the Normal Melting Point of Lead (600.5 K). What is the Temperature When the Resistance is 123.4 Ohm - CBSE (Science) Class 11 - Physics

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Question

The electrical resistance in ohms of a certain thermometer varies with temperature according to the approximate law:

Ro [1 + α (– To)]

The resistance is 101.6 Ω at the triple-point of water 273.16 K, and 165.5 Ω at the normal melting point of lead (600.5 K). What is the temperature when the resistance is 123.4 Ω?

Solution 1

Here, R0 = 101.6 Ω; T0 = 273.16 K Case (i) R1= 165.5 Ω; T= 600.5 K, Case (ii) R2 = 123.4 , T2 = ?

Using the relation R = R0[1 + α (T – T0)]

Case (i) 165.5 = 101.6 [1 + α (600.5 – 273.16)]

`alpha= (165.5 - 101.6)/(101.6xx(600.5-273.16)) = 63.9/(101.6xx327xx37)`

Case II    `123.4 = 101.6 [1 + alpha(T_2 - 273.16)]`

or `123.4 = 101.6 [1+ 63.9/(101.6xx327.34)(T_2-273.16)]`

`= 101.6 + 63.9/327.37 (T_2 - 273.16)`

or `T_2 = ((123.4-101.6)xx327.34)/63.9+ 273.16 = 111.67 + 273.16`

= 384.83 K

Solution 2

It is given that:

R0 [1 + α (– T0)] … (i)

Where,

R0 and T0 are the initial resistance and temperature respectively

R and T are the final resistance and temperature respectively

α is a constant

At the triple point of water, T0 = 273.15 K

Resistance of lead, R0 = 101.6 Ω

At normal melting point of lead, T = 600.5 K

Resistance of lead, R = 165.5 Ω

Substituting these values in equation (i), we get:

`R = R_0[1+alpha(T - T_0)]`

`165.5=101.6 [1+alpha(600.5 - 273.15)]`

`1.629 = 1 + alpha(327.35)`

`:.alpha = 0.629/327.35 = 1.92 xx 10^(-3) K^(-1)`

For resistance, `R_1= 123.4 Omega`

`R_1 = R_0[1+alpha(T-T_0)]`

Where T is the temperrature when the resistance of lead is `123.4 Omega`

`123.4 = 101.6[]1+1.92 xx 10^(-3)(T-273.15)]`

`1.214 = 1 + 1.92 xx 10^(-3)(T - 273.15)`

`0.214/(1.92xx10^(-3)) = T - 273.15`

:. T = 384.61 K

  Is there an error in this question or solution?

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 NCERT Solution for Physics Textbook for Class 11 (2018 to Current)
Chapter 11: Thermal Properties of Matter
Q: 3 | Page no. 294
Solution The Electrical Resistance in Ohms of a Certain Thermometer Varies with Temperature According to the Approximate Law the Resistance is 101.6 ω at the Triple-point of Water 273.16 K, and 165.5 Ohm at the Normal Melting Point of Lead (600.5 K). What is the Temperature When the Resistance is 123.4 Ohm Concept: Measurement of Temperature.
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