JEE Main 2025 Apr 4 Shift 2, Physics Q3: Thermal Expansion

JEE Main2025Apr 4, Shift 2Physics

Consider a rectangular sheet of solid material of length $ℓ = 9$ cm and width $d = 4$ cm. The coefficient of linear expansion is $α = 3.1 \times 1 0^{- 5} K^{- 1}$ at room temperature and one atmospheric pressure. The mass of sheet $m = 0.1$ kg and the specific heat capacity $C_{v} = 900 J k g^{- 1} K^{- 1}$ . If the amount of heat supplied to the material is $8.1 \times 1 0^{2}$ J then change in area of the rectangular sheet is :-

A
$2.0 \times 1 0^{- 6} m^{2}$
B
$3.0 \times 1 0^{- 7} m^{2}$
C
$6.0 \times 1 0^{- 7} m^{2}$
D
$4.0 \times 1 0^{- 7} m^{2}$

Solution

First find the temperature rise from the heat supplied:

$Δ T = \frac{Q}{m C _{v}} = \frac{8.1 \times 1 0 ^{2}}{0.1 \times 900} = 9$ K.

Initial area $A_{0} = ℓ \times d = 9 e x t c m \times 4 cm = 36 cm^{2} = 36 \times 1 0^{- 4} m^{2}$ .

For a 2-D expansion, the coefficient of area expansion is $β = 2 α$ . Hence

$Δ A = A_{0} \cdot 2 α \cdot Δ T = 36 \times 1 0^{- 4} \cdot 2 \cdot 3.1 \times 1 0^{- 5} \cdot 9$

$= 36 \times 9 \times 6.2 \times 1 0^{- 9} = 2008.8 \times 1 0^{- 9} \approx 2.0 \times 1 0^{- 6} m^{2}$ .

$∴ Δ A \approx 2.0 \times 1 0^{- 6} m^{2}$ .

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JEE Main 2025 Apr 4 Shift 2, Physics Q3: Thermal Expansion

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