Q3 of 26 Page 294

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

R = Ro [1 + α(T – 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?

Given,

Triple point of water, T0 = 273.16 K


Resistance at triple point, R0 = 101.6 Ω


Normal melting point of lead, T = 600.5 K


Resistance at normal melting point of lead, R = 165.5 Ω


Also,


R = R0[1+α(T-T0)]


Where, R0 is the initial resistance


Ris the final resistance


T0 is the initial temperature


T is the final temperature


∴ 165.5 Ω = (101.6 Ω)[1 + α(600.5 K - 273.16 K)]


⇒ 1+α(327.34) = 165.5/101.6


⇒ 1+327.34α = 1.629


⇒ 327.34α = 0.629


⇒ α = 0.629/327.34


⇒ α = 1.92 × 10-3 K-1


For R = 123.4 Ω,


123.4 Ω = (101.6 Ω)[1 + (1.92 × 10-3 K-1)(T - 273.16 K)]


⇒ 1 + (1.92 × 10-3 K-1)(T - 273.16 K) = 123.4/101.6


⇒ 1 + (1.92 × 10-3 K-1)(T - 273.16 K) = 1.214


⇒ (1.92 × 10-3 K-1)(T - 273.16 K) = 0.214


⇒ T - 273.16 K = 0.214/(1.92 × 10-3 K-1)


⇒ T – 273.16 K = 111.75 K


⇒ T = 111.75 K + 273.16 K


⇒ T = 384.91 K


More from this chapter

All 26 →
1

The triple points of neon and carbon dioxide are 24.57 K and 216.55 K respectively. Express these temperatures on the Celsius and Fahrenheit scales.

 2

Two absolute scales A and B have triple points of water defined to be 200 A and 350 B. What is the relation between TA and TB?

 4

Answer the following:

(a) The triple-point of water is a standard fixed point in modern thermometry.


Why? What is wrong in taking the melting point of ice and the boiling point of water as standard fixed points (as was originally done in the Celsius scale)?


(b) There were two fixed points in the original Celsius scale as mentioned above which were assigned the number 0°C and 100°C respectively. On the absolute scale, one of the fixed points is the triple-point of water, which on the Kelvin absolute scale is assigned the number 273.16 K. What is the other fixed point on this (Kelvin) scale?


(c) The absolute temperature (Kelvin scale) T is related to the temperature tc on the Celsius scale by


tc = T – 273.15


Why do we have 273.15 in this relation, and not 273.16?


(d) What is the temperature of the triple-point of water on an absolute scale whose unit interval size is equal to that of the Fahrenheit scale?

 5

Two ideal gas thermometers A and B use oxygen and hydrogen respectively. The following observations are made:


















Temperature



Pressure thermometer A



Pressure


thermometer B



Triple-point of water



1.250 × 105 Pa



0.200 × 105 Pa



Normal melting point of sulphur



1.797 × 105 Pa



0.287 × 105 Pa



(a) What is the absolute temperature of normal melting point of sulphur as read by thermometers A and B ?


(b) What do you think is the reason behind the slight difference in answers of thermometers A and B? (The thermometers are not faulty). What further procedure is needed in the experiment to reduce the discrepancy between the two readings?