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 × 10 5 Pa 0 . 200 × 10 5 Pa Normal melting point of sulphur 1 . 797 × 10 5 Pa 0 . 287 × 10 5 Pa What is the absolute temperature of normal melting point of sulphur as read by thermometer A and B ?

We know ideal gas equation is given by PV = nRT For thermometer A , T tr = 273 . 16 K , P tr = 1 . 250 × 10 5 Pa We have T = P P tr × T tr = 1 . 797 × 10 5 1 . 250 × 10 5 × 273 = 392 . 46 K For thermometer B , T tr = 273 . 16 K , P tr = 0 . 200 × 10 5 Pa We have T = P P tr × t tr = 0 . 287 × 10 5 × 273 . 16 0 . 200 × 10 5 = 391 . 98 K

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 × 10 5 Pa 0 . 200 × 10 5 Pa Normal melting point of sulphur 1 . 797 × 10 5 Pa 0 . 287 × 10 5 Pa What do you think is the reason for slightly different answers from A and B ?

We know ideal gas equation is given by PV = nRT For thermometer A , T tr = 273 . 16 K , P tr = 1 . 250 × 10 5 Pa We have T = P P tr × T tr = 1 . 797 × 10 5 1 . 250 × 10 5 × 273 = 392 . 46 K For thermometer B , T tr = 273 . 16 K , P tr = 0 . 200 × 10 5 Pa We have T = P P tr × t tr = 0 . 287 × 10 5 × 273 . 16 0 . 200 × 10 5 = 391 . 98 K The slight difference in the temperatures as read by two thermometers is due to the fact that oxygen and hydrogen do not behave like an ideal gas.

A metal rod, A of 25 cm length expands by, 0 . 050 cm when, its temperature is raised from 0 ° C to 100 ° C . Another rod, B of a different metal of 40 cm length expands by, 0 . 040 cm for the same rise in temperature. A third rod, C of 50 cm length is made up of pieces of rods, A and B placed end to end, expands by 0 . 03 cm on heating from 0 ° C to 50 ° C . Find the lengths of each portion of the composite rod.

Given, metal rod, A expands by 0 . 05 cm , when its temperature, θ is raised from 0 ° C to 100 ° C . We know that, ∆ l = l α ∆ θ . here ∆ l = Change in length l = Initial length α = Coefficient of linear expansion ∆ θ = Change in temperature For rod, A , 0 . 05 = 25 α A 100 - 0 ⇒ α A = 0 . 05 2500 = 2 × 10 - 5 per ° C Metal rod, B expands by 0 . 04 cm , when its temperature is raised from 0 ° C to 100 ° C . ⇒ 0 . 04 = 40 α B 100 - 0 ⇒ α B = 0 . 04 4000 = 1 × 10 - 5 per ° C . Now, a third rod, C of 50 cm length is made up of pieces of rods, A and B . Let's assume the length of A in rod C as x and the length of B in rod C as 50 - x cm . If, ∆ l 1 and ∆ l 2 are the change in lengths of A and B in rod C then, the total change in length of rod C is, ∆ l = ∆ l 1 + ∆ l 2 ⇒ 0 . 03 = x 2 × 10 - 5 50 - 0 + 50 - x 10 - 5 50 - 0 ⇒ 0 . 03 = x 10 - 3 + 50 - x 10 - 5 50 ⇒ 0 . 03 = x 10 - 3 + 50 10 - 5 50 - x 0 . 5 × 10 - 3 ⇒ 0 . 03 = x 0 . 5 × 10 - 3 + 0 . 025 ⇒ 5 × 10 - 3 = x 0 . 5 × 10 - 3 ∴ x = 10 cm and 50 - x = 50 - 10 cm = 40 cm . Therefore, the length of rod A in the composite rod is, 10 cm and the length of rod B in the composite rod is, 40 cm .

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Suppose you come across old scientific notes that describe a temperature scale called $Z$ on which the boiling point of water is $65.0 ° Z$ and the freezing point is $- 14.0 ° Z$ .

To what temperature on the Fahrenheit scale would a temperature of $T = - 98.0 ° Z$ correspond? Assume that the $Z$ scale is linear; that is, the size of a $Z$ degree is the same everywhere on the $Z$ scale.

Important Questions on Thermometry, Thermal Expansion and Calorimetry

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Physics

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PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 1 - Thermometry, Thermal Expansion and Calorimetry>ILLUSTRATION>Q 1.2

What will be the values of the following temperature on the Kelvin scale: $37 ° C$

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Physics

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PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 1 - Thermometry, Thermal Expansion and Calorimetry>ILLUSTRATION>Q 1.2

What will be the values of the following temperature on the Kelvin scale: $80 ° F$

EASY

Physics

IMPORTANT

PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 1 - Thermometry, Thermal Expansion and Calorimetry>ILLUSTRATION>Q 1.2

What will be the values of the following temperature on the Kelvin scale: $- 196 ° C$

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Physics

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PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 1 - Thermometry, Thermal Expansion and Calorimetry>ILLUSTRATION>Q 1.3

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	$1.250 \times 10^{5} Pa$	$0.200 \times 10^{5} Pa$
Normal melting point of sulphur	$1.797 \times 10^{5} Pa$	$0.287 \times 10^{5} Pa$

What is the absolute temperature of normal melting point of sulphur as read by thermometer $A$ and $B ?$

MEDIUM

Physics

IMPORTANT

PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 1 - Thermometry, Thermal Expansion and Calorimetry>ILLUSTRATION>Q 1.3

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	$1.250 \times 10^{5} Pa$	$0.200 \times 10^{5} Pa$
Normal melting point of sulphur	$1.797 \times 10^{5} Pa$	$0.287 \times 10^{5} Pa$

What do you think is the reason for slightly different answers from $A$ and $B ?$

MEDIUM

Physics

IMPORTANT

PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 1 - Thermometry, Thermal Expansion and Calorimetry>ILLUSTRATION>Q 1.4

A brass rod of length $50 cm$ and diameter $3 mm$ is joined to a steel rod of the same length and diameter. What is the change in length of the combined rod at $250 ° C$ , if the original lengths are at $40 .0 ° C$ ? Is there a ‘thermal stress’ developed at the junction? The ends of the rod are free to expand (Co-efficient of linear expansion of brass is $2 .0 \times 10^{- 5} K^{- 1}$ and steel is $1 .2 \times 10^{- 5} K^{- 1}$ )

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Physics

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PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 1 - Thermometry, Thermal Expansion and Calorimetry>ILLUSTRATION>Q 1.5

An isosceles triangle is formed with a thin rod of length $l_{1}$ and coefficient of linear expansion $α_{1}$ , as the base and two thin rods each of length $l_{2}$ and coefficient of linear expansion $α_{2}$ as the two sides. If the distance between the apex and the midpoint of the base remain unchanged as the temperature varies, show that $\frac{l_{1}}{l_{2}} = 2 \sqrt{\frac{α_{2}}{α_{1}}}$ .

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MEDIUM

Physics

IMPORTANT

PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 1 - Thermometry, Thermal Expansion and Calorimetry>ILLUSTRATION>Q 1.6

A metal rod,

A

25 cm

length expands by,

0.050 cm

when, its temperature is raised from

0 ° C

100 ° C

. Another rod,

B

of a different metal of

40 cm

length expands by,

0.040 cm

for the same rise in temperature. A third rod,

C

50 cm

length is made up of pieces of rods,

A

and

B

placed end to end, expands by

0.03 cm

on heating from

0 ° C

50 ° C

. Find the lengths of each portion of the composite rod.

Important Questions on Thermometry, Thermal Expansion and Calorimetry

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