CBSE Class 12 Physics Thermal Expansion Theory and Examples

CBSE Class 12 Physics Thermal Expansion Theory and Examples. Please refer to the examination notes which you can use for preparing and revising for exams. These notes will help you to revise the concepts quickly and get good marks.


Solids are made of atoms and molecules. At a given temperature, the atoms and molecules are placed at some equilibrium distance. When heat is supplied to solid, the interatomic separation increases by which there is an expansion of solids. This expansion can be in terms of length/area/volume.



(i) Almost all solids expand on heating. On increasing the temperature of a solid, its length increases. This change in length of a solid on heating is called linear expansion.
(ii) Coefficient of linear expansion is defined as fractional increase in length per ºC rise in temperature. If
l is the length of the rod at T K and as the temperature is changed to T + ΔT its length becomes l+ Δl, so coefficient of linear expansion is given by



(iii) Unit of α is Per Kelvin or Per ºC. It is positive for metals except carbon. The value of α is negative for plastic because in plastic when the temperature increases, length decreases.
(iv)The numerical value of α is same in both the units i.e. in Per Kelvin or Per ºC
(v) If α is coefficient of linear expansion at t1ºC.
l1 = length of the rod at t1ºC
l2 = length of the rod at t2ºC
               l2 =l1[1 + α(t2 – t1)]
t may be in any unit ºC or ºK because in the formula there is a difference of temperature which remains same for ºC or ºK.
(vi) If length of the rod is
l0 at 0ºC and lt at tºC than
                lt = l0 [1 + α (t – 0)]
        lt = l0(1 + αt)

where α is temperature coefficient of linear expansion at 0ºC. Here t should be in ºC only because initial temperature is taken as 0ºC.


From the above tree, it is clear that the thermal expansion of solid is classified into three categories.
(1) Linear expansion of solids
(2) Superficial expansion of solids
(3) Cubical expansion of solids
Now we shall discuss these topics one by one.


3.1 Differential expansion of two solid rod
(1) Suppose there are two rods of length
l1 and l2.The first rod is kept on the other such that the initial separation between the free ends of the
rod is S = 
l2 – l1

Both the rods are initially at a temperature of t1ºC. On heating the entire system, the temperature increases to t2 such that the length of both the rod increases. So, if the new length of the rod be




3.2 Radius of Bimetallic strip
If two strips of different metals are welded together to form a bimetallic strip, when heated uniformly it bends in the form of an arc, the metal with greater coefficient of linear expansion lies on convex side. The radius of arc thus formed by bimetal is


Differential expansion of two solid rods

Ex. 1 The length of the steel rod which would have the same difference in length with a copper rod of length 24cm at all temperatures. (αcopper = 18 × 10–6 k–1, αsteel = 12 × 10–6 k–1)

is –
(A) 20 cm (B) 18 cm (C) 24 cm (D) 36 cm


Ex. 2 A metal sheet with a circular hole is heated. The hole

(A) Gets larger
(B) Gets smaller
(C) Remains of the same size
(D) Gets deformed
Sol. (A) When a body is heated, the distance between any two points on it increases. So due to thermal expansion of solids, the hole gets larger.

Ex. 3 Two identical rectangular strips one of copper and other of steel are riveted together to form a bimetallic strip (αcopper > αsteel). On heating this strip will

(A) Remains straight
(B) Bend with copper on convex side
(C) Bend with steel on convex side
(D) Get twisted
Sol. (B) When a bimetallic strip of different metals is heated, the strip bends due to unequal linear expansion of the two metals. The strip will bend with metal of greater α on the convex side i.e. outer side.

3.3 Thermal stress

(1) When a rod is heated or cooled, it expands or contracts. It is turned as free expansion of the rod 


Please click on below link to download pdf file for CBSE Class 12 Physics Thermal Expansion Theory and Examples.


Click to View or Download pdf file
Click for more Physics Study Material

Latest NCERT & CBSE News

Read the latest news and announcements from NCERT and CBSE below. Important updates relating to your studies which will help you to keep yourself updated with latest happenings in school level education. Keep yourself updated with all latest news and also read articles from teachers which will help you to improve your studies, increase motivation level and promote faster learning

Board Exams Class 10 and Class 12 Datesheet 2020

CBSE has announced the datesheet for the remaining exams of class 10 and class 12 exams. The exams are going to start in July. The class 10 and 12th board exams will be conducted for the remaining 29 papers from July 1 to July 15, 2020, at various centers nominated by...

Important announcement regarding rescheduling of Class 10 and 12 Board Exams

CBSE Board Exams 2020: Here's when Board will organize the CBSE Class X and Class XII Board Exams. All the candidates appearing for CBSE Standard X and Standard XII Board Exams 2020 can cross check the essential notice released by the board concerning rearrangement of...

CBSE Board Exams in July Press Release

CBSE has released press note for the dates for the CBSE Board exams for Class 10. CBSE said “With regards to conduct of Class X examinations several queries are being received by the CBSE. In this context, it is once again reiterated that remaining examinations of...

CBSE Boards Answer Sheet Evaluation Class 10 and Class 12

HRD Minister Ramesh Pokhriyal, through a video conference with all the education ministers of the state, discussed the further steps to be taken to smoothen the education process during the Covid-19 lockdown. The most important topic which was discussed repeatedly on...

Art Integrated Project work for classes 1 to 10

CBSE Board has decided to introduce Art-Integrated Project work for classes I to X to promote Art-Integrated Learning in schools to make teaching learning Competency-Based and joyful. As part of this, at least one Art-Integrated Project in each subject shall be taken...

Class 10 Board Exams to be held

The CBSE board has announced that there is no change in the decision of conducting the CBSE board exams for the 29 subjects, which were canceled due to coronavirus crisis. So when the lockdown gets relaxed completely, the board will conduct the exams for the students,...

Studies Today