Thermal Expansion | JEE Main previous year questions with Solutions

Q 1 :

Consider a rectangular sheet of solid material of length $l$ = 9 cm and width d = 4 cm. The coefficient of linear expansion is $α = 3.1 \times 10^{- 5} K^{- 1}$ at room temperature and one atmospheric pressure. The mass of sheet m = 0.1 kg and the specific heat capacity $C_{v} = 900 J {kg}^{- 1} K^{- 1}$ . If the amount of heat supplied to the material is $8.1 \times 10^{2} J$ then change in area of the rectangular sheet is: [2025]

$2.0 \times 10^{- 6} m^{2}$
$3.0 \times 10^{- 7} m^{2}$
$6.0 \times 10^{- 7} m^{2}$
$4.0 \times 10^{- 7} m^{2}$

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(1)

$Q = m c △ T$

$8.1 \times 10^{2} = 900 \times 0.1 \times △ T \Rightarrow △ T = 9 K$

$△ A = A \cdot 2 α △ T$

$= 36 \times 2 \times 3.1 \times 10^{- 5} \times 9 \times 10^{- 4} = 2 \times 10^{- 6} m^{2}$

Q 2 :

A hole is drilled in a metal sheet. At $27 ° C$ , the diameter of the hole is 5 cm. When the sheet is heated to $177 ° C$ , the change in the diameter of the hole is $d \times 10^{- 3} cm$ . The value of $d$ will be _______ if the coefficient of linear expansion of the metal is $1.6 \times 10^{- 5} / ° C$ . [2023]

(12)

$d_{0} at 27 ° C and d_{1} at 177 ° C$

$d_{1} = d_{0} (1 + α Δ T)$

$(d_{1} - d_{0}) = 5 \times 1.6 \times 10^{- 5} \times 150 cm = 12 \times 10^{- 3} cm$

Q 3 :

A thin rod having a length of 1 m and area of cross-section $3 \times 10^{- 6} m^{2}$ is suspended vertically from one end. The rod is cooled from $210 ° C$ to $160 ° C$ . After cooling, a mass M is attached at the lower end of the rod such that the length of the rod again becomes 1 m. Young's modulus and coefficient of linear expansion of the rod are $2 \times 10^{11} {Nm}^{- 2}$ and $2 \times 10^{- 5} K^{- 1}$ , respectively. The value of M is ______ kg. (Take $g = 10 {ms}^{- 2}$ ) [2023]

(60)

$If Δ l is decrease in length of rod due to decrease in temperature$

$Δ l = l α Δ T$

$α = 2 \times 10^{- 5} K^{- 1}$

$Δ T = (210 - 160) = 50 K$

$Δ l = 1 \times 2 \times 10^{- 5} \times 50 = 10^{- 3} m$

$Young's Modulus = Y = \frac{F / A}{Δ l / l}, A = 3 \times 10^{- 6} m^{2}$

$2 \times 10^{11} = \frac{M g / 3 \times 10^{- 6}}{10^{- 3} / 1}$

$M g = 2 \times 10^{11} \times 3 \times 10^{- 9} = 6 \times 10^{- 2}$

$\Rightarrow M = 60 kg$

Q 4 :

An aluminium and steel rods having same lengths and cross-sections are joined to make total length of 120 cm at 30°C. The coefficient of linear expansion of aluminium and steel are $24 \times 10^{- 6} / ° C and 1.2 \times 10^{- 5} / ° C$ respectively. The length of this composite rod when its temperature is raised to 100°C, is ________ cm. [2026]

120.20
120.06
120.03
120.15

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(4)

$ℓ_{final} = ℓ_{0} (1 + α_{A} Δ T) + ℓ_{0} (1 + α_{B} Δ T)$

$= ℓ_{0} [2 + (α_{A} + α_{B}) Δ T]$

$= 60 [2 + (36 \times 10^{- 6}) \times 70]$

$= 60 [2 + 0.0025]$

$= 120.15 cm$

Q 5 :

A brass wire of length 2 m and radius 1 mm at $27 ° C$ is held taut between two rigid supports. Initially, it was cooled to a temperature of $- 43 ° C$ creating a tension T in the wire. The temperature to which the wire has to be cooled in order to increase the tension in it to 1.4T, is _________ ${}^{\circ}C$ . [2026]

- 80
- 65
- 71
- 86

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(3)

$T = α Y A (27 - (- 43)) . ..(i)$

$1.4 T = α Y A (27 - θ) ...(ii)$

$Using (ii)/(i):$

$1.4 = \frac{27 - θ}{70}$

$27 - θ = 98 ∴ θ = - 71 ° C$

Q 6 :

Which of the following best represents the temperature versus heat supplied graph for water, in the range of $- 20 ° C t o 120 ° C$ ? [2026]

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(2)

$- 20 ° C to 0 ° C: q = m s_{ice} Δ T$ $At 0 ° C, phase change takes place.$

$0 ° C to 100 ° C: q = m s_{water} Δ T$ $At 100 ° C, phase change takes place.$

Q 7 :

Two large holes are cut in a metal sheet as shown. If this is heated, which distance will decrease:

BC
AB
AC
None of these

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(4)

Distance between any two points when only increase.

Q 8 :

The temperature of a metal strip having coefficient of linear expansion $α$ is increased from $T_{1}$ to $T_{2}$ resulting in increase of its length by $Δ L_{1}$ . The temperature is further increased from $T_{2}$ to $T_{3}$ such that the increase in its length is $Δ L_{2}$ .

Given $T_{3} + T_{1} = 2 T_{2}$ and $T_{2} - T_{1} = Δ T$ , the value of $Δ L_{2}$ is ______. [2026]

$Δ L_{1} [1 + 2 α^{2} {(Δ T)}^{2}]$
$Δ L_{1} [1 + α^{2} {(Δ T)}^{2}]$
$Δ L_{1} [1 + 2 α Δ T]$
$Δ L_{1} [1 + α Δ T]$

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(4)

$Δ L_{1} = α L_{1} Δ T$

$Δ L_{2} = (L_{1} + Δ L_{1}) (T_{3} - T_{2})$

$Δ L_{2} = (L_{1} + Δ L_{1}) Δ T$

$Δ L_{2} = (\frac{Δ L_{1}}{α Δ T} + Δ L_{1}) α Δ T$

$Δ L_{2} = Δ L_{1} [1 + α Δ T]$

Topic Question Set

Q 6 :

Which of the following best represents the temperature versus heat supplied graph for water, in the range of $- 20 ° C t o 120 ° C$ ? [2026]

Q 7 :

Two large holes are cut in a metal sheet as shown. If this is heated, which distance will decrease:

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Topic Question Set

Q 2 : A hole is drilled in a metal sheet. At 27°C, the diameter of the hole is 5 cm. When the sheet is heated to 177°C, the change in the diameter of the hole is d×10-3 cm. The value of d will be _______ if the coefficient of linear expansion of the metal is 1.6×10-5/°C. [2023]

Q 6 : Which of the following best represents the temperature versus heat supplied graph for water, in the range of -20°C to 120°C? [2026]

Q 7 : Two large holes are cut in a metal sheet as shown. If this is heated, which distance will decrease:

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Q 6 :

Which of the following best represents the temperature versus heat supplied graph for water, in the range of $- 20 ° C t o 120 ° C$ ? [2026]

Q 7 :

Two large holes are cut in a metal sheet as shown. If this is heated, which distance will decrease: