groups mcq sq lq marksmarks
TRANSCRIPT
Class 11: Introduction of Syllabus
Groups
MCQ
SQ
LQ
MarksMarks
Mechanics 5(5) 1/2 = (5) 1 +1/2 = (16) 26 10
Heat and Thermodynamics
0 3(15) 0 15 9
Waves and Optics
4 1/2 = (5) 0 9 28
Electricity and Magnetism
1 3(15) 0 16 28
Modern Physics 1 0 1(8) 9 75
Marks 11 40 24 75
Heat and Temperature
Heat is a form of energy, the flow of which gives the sensation of hotness or coldness to our body. Its SI unit is Joule
and CGS unit is Calorie. Temperature is the degree of hotness or coldness of a body. Its SI unit is Kelvin and CGS unit
is Centigrade or Celsius. Heat is measured by total K.E. of the molecules of a body while temperature is measured in
terms of average K.E. of the molecules of a body. However more heat energy in a body does not necessarily mean that
it is at higher temperature. Higher the average K.E., greater the temperature of a body.
Thermal Equilibrium and Zeroth law:
When two bodies at different temperatures are placed in contact, molecules of a body at higher temperature with more
average K.E. give up some energy to the less energetic molecules of a cold body so that increase in energy of
molecules takes place towards cold body while decrease in energy takes place towards hot body and due to this reason
it is called that heat flows from hot to cold body. The change in K.E. of molecules takes place until average K.E. of
molecules or temperature of both bodies reach to the same value. This stage is called thermal equilibrium. Thus
temperature is a physical quantity which determines the direction of heat flow while only by knowing the heat
contained in two bodies we cannot predict the direction of heat flow.
Zeroth law of thermodynamics states that if two bodies are separately in thermal equilibrium with third body then
those bodies are also to be in thermal equilibrium. For eg. measuring our body temperature by using thermometer. To
know about the thermal equilibrium condition we compare their temperature readings. Two bodies in thermal
equilibrium must have the same temperature while they may or may not have the same amount of heat. On the basis of
zeroth law, temperature is that thermal property which determines whether two bodies are in thermal equilibrium or
not.
Temperature Scales:
Consider four identical thermometers scaled
on Celsius, Fahrenheit, Reaumer and Kelvin
as shown in Fig. C1(a). If all are used to
measure the temperature of same substance,
they rise up to the height but show different
readings. The conversion relation between
them is obtained by equating the common
term given below for all thermometers
π ππππππ ππ π‘βπππππππ‘ππ β πΏππ€ππ πππ₯ππ πππππ‘
πππππ πππ₯ππ πππππ‘ β πΏππ€ππ πππ₯ππ πππππ‘
So, πΆβ0
100β0=
πΉβ32
212β32=
π β0
80β0=
πΎβ273
373β273
Q.1. At what temperature (i) Celsius and Fahrenheit scales show equal readings? (ii) Kelvin scale shows double
reading than that of Fahrenheit scale? (A: -400C, 176.70For 353.4K)
Q.2. A faulty thermometer with its lower and upper fixed points 20C and 980C respectively reads temperature of a body
400C. What will be the correct temperature of a body in centigrade unit? (Hint:40β2
98β2=
π₯β0
100β0) (A: 39.580C)
Q.3. A faulty thermometer with its lower and upper fixed points -20C and 1020C respectively reads temperature of a
body 200C. What will be the correct temperature of a body in Fahrenheit scale? (Hint:20+2
102+2=
πΉβ32
180) (A: 70.070F)
Alternatively, first we can convert in correct Celsius reading and then convert in Fahrenheit scale.
)(1. aCFigβ΄
πΆ
5=
πΉ β 32
9=
π
4=
πΎ β 273
5
Thermal Expansion:
The increase in size of a body due to heating is called thermal expansion. There are three types of thermal
expansions for solids. They are: 1) linear expansion 2) superficial expansion and 3) cubical expansion
1) Linear Expansion:The increase in length of a one dimensional linear solid for eg. wire or rod due to
heating is called linear expansion.
Let us consider a wire or rod of length π1at temperature π10πΆwhich is
heated upto temperature π20πΆ at which its length is π2as shown in
Fig.C2(a). Experiment shows that
Increase in length (π2 β π1) β rise in temperature (π2 β π1)
Again, Increase in length (π2 β π1) β Initial length (π1)
Combining both, Increase in length (π2 β π1) β rise in temperature (π2 β π1) Γ Initial length (π1)
Or, π2 β π1 β π1 Γ (π2 β π1)
Or, π2 β π1 = πΌ π1 Γ (π2 β π1) ; where Ξ± is called coefficient of linear expansion or linear expansivity.
Linear Expansivity (Ξ±): The coefficient of linear expansion or linear expansivity is given by
πΌ =π2βπ1
π1(π2βπ1)Where π1is initial length, (π2 β π1) is increase in length, (π2 β π1)is rise in temperature.
Therefore, coefficient of linear expansion or linear expansivity is defined as the increase in length per
unit original length per unit rise in temperature. Its unit is 0C-1orK-1. Alpha (Ξ±) is same for given material
and it has different values for different materials. Even if original length and rise in temperature are
different, increase in length is also different and hence alpha (Ξ±) remains same for a given material.
2) Superficial Expansion:The increase in area of a two dimensional body for eg. metal sheet due to
heating is called superficial expansion.
Let us consider a bodyof areaπ΄1at temperature π10πΆwhich is heated
upto temperature π20πΆ at which its area is π΄2as shown in Fig. C2(b).
Experiment shows that
Increase in area(π΄2 β π΄1) β rise in temperature (π2 β π1)
Again, Increase in area(π΄2 β π΄1) β Initial area(π΄1)
Combining both,
Increase in area(π΄2 β π΄1) β rise in temperature (π2 β π1) Γ Initial area(π΄1)
Or, π΄2 β π΄1 β π΄1 Γ (π2 β π1)
Or, π΄2 β π΄1 = π½ π΄1 Γ (π2 β π1) ; where Ξ² is called coefficient of superficial expansion or superficial
expansivity.
Superficial Expansivity (Ξ²):The coefficient of superficial expansion or superficial expansivity is given
by π½ =π΄2βπ΄1
π΄1(π2βπ1)Where π΄1is initial area, (π΄2 β π΄1) is increase in area, (π2 β π1) is rise in temperature.
11,l
22 ,l
12 ll β
)(2. aCFig
11,A
22 ,A
)(2. bCFig
Therefore, coefficient of superficial expansion or superficial expansivity is defined as the increase in area
per unit original area per unit rise in temperature. Its unit is 0C-1, K-1. Beta (Ξ²) is same for a given
material.
3) Cubical Expansion:The increase in volume of a three dimensional body for eg. cube due to heating
is called superficial expansion.
Let us consider a bodyof volumeπ1at temperature π10πΆwhich is
heated upto temperature π20πΆ at which its volume is π2as shown in
Fig. C2(c). Experiment shows that
Increase in volume(π2 β π1) β rise in temperature (π2 β π1)
Again, Increase in volume(π2 β π1) β Initial volume(π1)
Combining both,
Increase in volume(π2 β π1) β rise in temperature (π2 β π1) Γ Initial volume(π1)
Or, π2 β π1 β π1 Γ (π2 β π1)
Or, π2 β π1 = πΎ π1 Γ (π2 β π1) ; where Ξ³ is called coefficient of cubical expansion or cubical
expansivity.
Cubical Expansivity (Ξ³): The coefficient of cubical expansion or cubical expansivity is given by
πΎ =π2βπ1
π1(π2βπ1)Where π1is initial volume, (π2 β π1) is increase in volume, (π2 β π1)is rise in
temperature.
Therefore, coefficient of cubical expansion or cubical expansivity is defined as the increase in volume
per unit original volume per unit rise in temperature. Its unit is 0C-1, K-1. Gamma (Ξ³) is same for a given
material.
Relation between Ξ±, Ξ² and Ξ³:
1) Ξ± and Ξ²:
Let us consider a square sheet of area π΄1at temperature π10πΆ such that length
of each sideπ1. When it is heated, its area becomes π΄2at temperature π2ππΆ
such that length of each sideπ2 as shown in Fig.C2(d).
Then, π΄1 = π12 β¦ β¦ β¦ . . (1)
π΄2 = π22 β¦ β¦ β¦ . . (2)
The coefficient of linear expansion is given by πΌ =π2βπ1
π1(π2βπ1)
Or, πΌπ1(π2 β π1) = π2 β π1
Or, π2 = π1πΌ(π2 β π1) + π1
Similarly, coefficient of superficial expansion is given by π½ =π΄2βπ΄1
π΄1(π2βπ1)
Or, π½π΄1(π2 β π1) = π΄2 β π΄1
)(2. cCFig
11,V
22 ,V
11,A
22 ,A
)(2. dCFig
1l
2l
π2 = π1{1 + πΌ(π2 β π1)} β¦ β¦ β¦ (3)
Or, π΄2 = π΄1πΌ(π2 β π1) + π΄1
Putting equation (1) and (2) in equation (4)π22 = π1
2{1 + π½(π2 β π1} β¦ β¦ β¦ β¦ (5)
Putting equation (3) in (5), we get π12{1 + πΌ(π2 β π1)}2= π1
2{1 + π½(π2 β π1}
Or, 1 + 2πΌ(π2 β π1) + πΌ2(π2 β π1)2 = 1 + π½(π2 β π1)
Since, Ξ± is very small for any material, the term containing Ξ±2 is neglected. Then,
2πΌ(π2 β π1) = π½(π2 β π1)
2) Ξ± and Ξ³:
Let us consider a cube of volume V1 at temperature ΞΈ10C such that
length of each side is π1. When it is heated its volume becomes V2
at temperature ΞΈ20C and length of each side is π2 as shown in Fig.
C2(e).
Then, π1 = π13 β¦ β¦ β¦ . . (1)
π2 = π23 β¦ β¦ β¦ . . (2)
The coefficient of linear expansion is given by πΌ =π2βπ1
π1(π2βπ1)
Or, πΌπ1(π2 β π1) = π2 β π1
Or, π2 = π1πΌ(π2 β π1) + π1
Similarly, coefficient of cubical expansion is given by πΎ =π2βπ1
π1(π2βπ1)
Or, πΎπ1(π2 β π1) = π2 β π1
Or, π2 = π1πΌ(π2 β π1) + π1
Putting equation (1) and (2) in equation (4) π23 = π1
3{1 + πΎ(π2 β π1} β¦ β¦ β¦ β¦ (5)
Putting equation (3) in (5), we get π13{1 + πΌ(π2 β π1)}3= π1
3{1 + πΎ(π2 β π1}
Or, 1 + 3πΌ(π2 β π1)2 + 3πΌ2(π2 β π1) + πΌ3(π2 β π1)3 = 1 + πΎ(π2 β π1)
Since, Ξ± is very small for any material, we can neglect the terms containing higher order of alpha, Then,
3πΌ(π2 β π1) + 0 + 0 = πΎ(π2 β π1)
π΄2 = π΄1{1 + π½ (π2
β π1)} β¦ β¦ β¦ (4)
β΄ Ξ² = 2πΌ
11,V
22 ,V
)(2. eCFig
1l
2l
π2 = π1{1 + πΌ(π2 β π1)} β¦ β¦ β¦ (3)
π2 = π1{1 + πΎ(π2 β π1)} β¦ β¦ β¦ (4)
β΄ πΎ = 3πΌ
Combining both relations,
Determination of alpha (Ξ±): Pullingerβs Apparatus Method:
An experimental arrangement to
determine linear expansivity of any
material is as shown in Fig.C2 (f).
Rod AB of length π1is taken at initial
temperatureπ10πΆ. It is placed in an
evacuated metallic tube of which
three holes are used for steam inlet,
steam outlet and thermometer (T).
Lower end B of rod is fixed while
upper end A is free to expand.
Battery, Galvanometer and Key are
used to check the connection between
spherometer and point A of rod.
Spherometer is used to measure the
expansion of rod.
When spherometer touches point A of rod reading R1 of spherometer is noted. Some gap is left between
spherometer and point A of rod to provide space for expansion. Now steam is passed through steam inlet
until the final temperature π2ππΆ is noted and expansion is measured by connecting spherometer leg with
point A of rod where reading of spherometer is R2. Now, R2 β R1 = Increase in length
When spherometer touches point A of rod galvanometer shows deflection. Now, coefficient of linear
expansion or linear expansivity is given by
πΌ =πΌππππππ π ππ πππππ‘β
πΌπππ‘πππ πππππ‘β Γ π ππ π ππ π‘πππππππ‘π’ππ=
π 2 β π 1
π1(π2 β π1)
By using this expression we can determine linear expansivity of any material. Simillarly we can calculate
superficial and cubical expansivity of a material by using π½ = 2πΌ πππ πΎ = 3πΌ
πΌ =π½
2=
πΎ
3
)(2. fCFig
