NCERT Solutions Class 11 Physics Chapter 11 Thermal Properties Of Matter Download In Pdf

Chapter 11 Thermal Properties of Matter Download in pdf

**Question 11.1** 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.

**Question 11.2** 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 ?

**
Question 11.3** 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 ?

**Question 11.4** 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 ?

**Question 11.5** Two ideal gas thermometers A and B use oxygen and hydrogen respectively. The
following observations are made :
Temperature Pressure Pressure
thermometer A thermometer B
Triple-point of water 1.250 × 105 Pa 0.200 × 105 Pa
Normal melting point 1.797 × 105 Pa 0.287 × 105 Pa
of sulphur
(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 ?

**Question 11.6** A steel tape 1m long is correctly calibrated for a temperature of 27.0 °C. The
length of a steel rod measured by this tape is found to be 63.0 cm on a hot day
when the temperature is 45.0 °C. What is the actual length of the steel rod on that
day ? What is the length of the same steel rod on a day when the temperature is
27.0 °C ? Coefficient of linear expansion of steel = 1.20 × 10–5 K–1 .

**Question 11.7** A large steel wheel is to be fitted on to a shaft of the same material. At 27 °C, the
outer diameter of the shaft is 8.70 cm and the diameter of the central hole in the
wheel is 8.69 cm. The shaft is cooled using ‘dry ice’. At what temperature of the
shaft does the wheel slip on the shaft? Assume coefficient of linear expansion of
the steel to be constant over the required temperature range :
αsteel = 1.20 × 10–5 K–1.

**Question 11.8** A hole is drilled in a copper sheet. The diameter of the hole is 4.24 cm at 27.0 °C.
What is the change in the diameter of the hole when the sheet is heated to 227 °C?
Coefficient of linear expansion of copper = 1.70 × 10–5 K–1.

**Question 11.9 **A brass wire 1.8 m long at 27 °C is held taut with little tension between two rigid
supports. If the wire is cooled to a temperature of –39 °C, what is the tension
developed in the wire, if its diameter is 2.0 mm ? Co-efficient of linear expansion
of brass = 2.0 × 10–5 K–1; Young’s modulus of brass = 0.91 × 1011 Pa.

**Question 11.10** A brass rod of length 50 cm and diameter 3.0 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 = 2.0 × 10–5 K–1, steel = 1.2 × 10–5 K–1 ).

**Question 11.11** The coefficient of volume expansion of glycerin is 49 × 10–5 K–1. What is the fractional
change in its density for a 30 °C rise in temperature ?

**Question 11.12** A 10 kW drilling machine is used to drill a bore in a small aluminium block of mass
8.0 kg. How much is the rise in temperature of the block in 2.5 minutes, assuming
50% of power is used up in heating the machine itself or lost to the surroundings.
Specific heat of aluminium = 0.91 J g–1 K–1.

**Question 11.13** A copper block of mass 2.5 kg is heated in a furnace to a temperature of 500 °C
and then placed on a large ice block. What is the maximum amount of ice that
can melt? (Specific heat of copper = 0.39 J g–1 K–1; heat of fusion of water
= 335 J g–1 ).

**Question 11.14 **In an experiment on the specific heat of a metal, a 0.20 kg block of the metal at
150 °C is dropped in a copper calorimeter (of water equivalent 0.025 kg) containing
150 cm3 of water at 27 °C. The final temperature is 40 °C. Compute the specific heat of the metal. If heat losses to the surroundings are not negligible, is your
answer greater or smaller than the actual value for specific heat of the metal ?

**Question 11.15** Given below are observations on molar specific heats at room temperature of some
common gases.
Gas Molar specific heat (Cv )
(cal mo1–1 K–1)
Hydrogen 4.87
Nitrogen 4.97
Oxygen 5.02
Nitric oxide 4.99
Carbon monoxide 5.01
Chlorine 6.17
The measured molar specific heats of these gases are markedly different from
those for monatomic gases. Typically, molar specific heat of a monatomic gas is
2.92 cal/mol K. Explain this difference. What can you infer from the somewhat
larger (than the rest) value for chlorine ?

**Question 11.16** Answer the following questions based on the P-T phase diagram of carbon dioxide:

(a) At what temperature and pressure can the solid, liquid and vapour phases of
CO2 co-exist in equilibrium ?

(b) What is the effect of decrease of pressure on the fusion and boiling point of
CO2 ?

(c) What are the critical

temperature and pressure for CO2 ? What is their
significance ?

(d) Is CO2 solid, liquid or gas at (a) –70 °C under 1 atm, (b) –60 °C under 10 atm,
(c) 15 °C under 56 atm ?

**Question 11.17 **Answer the following questions based on the P – T phase diagram of CO2:

(a) CO2 at 1 atm pressure and temperature – 60 °C is compressed isothermally.
Does it go through a liquid phase ?

(b) What happens when CO2 at 4 atm pressure is cooled from room temperature
at constant pressure ?

(c) Describe qualitatively the changes in a given mass of solid CO2 at 10 atm
pressure and temperature –65 °C as it is heated up to room temperature at
constant pressure.

(d) CO2 is heated to a temperature 70 °C and compressed isothermally. What
changes in its properties do you expect to observe ?

**Question 11.18** A child running a temperature of 101°F is given an antipyrin (i.e. a medicine that
lowers fever) which causes an increase in the rate of evaporation of sweat from his
body. If the fever is brought down to 98 °F in 20 min, what is the average rate of
extra evaporation caused, by the drug. Assume the evaporation mechanism to be
the only way by which heat is lost. The mass of the child is 30 kg. The specific
heat of human body is approximately the same as that of water, and latent heat of
evaporation of water at that temperature is about 580 cal g–1.

**Question 11.19** A ‘thermacole’ icebox is a cheap and efficient method for storing small quantities
of cooked food in summer in particular. A cubical icebox of side 30 cm has a
thickness of 5.0 cm. If 4.0 kg of ice is put in the box, estimate the amount of ice
remaining after 6 h. The outside temperature is 45 °C, and co-efficient of thermal
conductivity of thermacole is 0.01 J s–1 m–1 K–1. [Heat of fusion of water = 335 × 103
J kg–1]

**Question 11.20** A brass boiler has a base area of 0.15 m2 and thickness 1.0 cm. It boils water at the
rate of 6.0 kg/min when placed on a gas stove. Estimate the temperature of the part of the flame in contact with the boiler. Thermal conductivity of brass = 109 J s–1 m–1
K–1 ; Heat of vaporisation of water = 2256 × 103 J kg–1.

**Question 11.21** Explain why :

(a) a body with large reflectivity is a poor emitter

(b) a brass tumbler feels much colder than a wooden tray on a chilly day

(c) an optical pyrometer (for measuring high temperatures) calibrated for an ideal
black body radiation gives too low a value for the temperature of a red hot
iron piece in the open, but gives a correct value for the temperature when the
same piece is in the furnace

(d) the earth without its atmosphere would be inhospitably cold

(e) heating systems based on circulation of steam are more efficient in warming
a building than those based on circulation of hot water

**Question 11.22** A body cools from 80 °C to 50 °C in 5 minutes. Calculate the time it takes to cool
from 60 °C to 30 °C. The temperature of the surroundings is 20 °C.

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- Chapter 1 Physical World
- Chapter 2 Units And Measurement
- Chapter 3 Motion In A Straight Line
- Chapter 4 Motion In A Plane
- Chapter 5 Laws Of Motion
- Chapter 7 Systems of Particles and Rotational Motion
- Chapter 6 Work Energy and Power
- Chapter 8 Gravitation
- Chapter 9 Mechanical Properties Of Solids
- Chapter 10 Mechanical Properties Of Fluids
- Chapter 11 Thermal Properties of Matter
- Chapter 12 Thermodynamics
- Chapter 13 Kinetic Theory
- Chapter 14 Oscillations
- Chapter 15 Waves

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