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 × 10⁻⁵ K⁻¹ at room temperature and one atmospheric pressure. The mass of sheet m = 0.1 kg and the specific heat capacity Cv = 900 J kg⁻¹ K⁻¹. If the amount of heat supplied to the material is 8.1 × 10² J then change in area of the rectangular sheet is: (a) 2.0 × 10⁻⁶ m² (b) 6.0 × 10⁻⁷ m² (c) 3.0 × 10⁻⁷ m² (d) 4.0 × 10⁻⁷ m²

Answer: (a). Δ T = Q/mc = (810)/(0.1 × 900) = 9 K A = 9 × 4 = 36 cm² = 36×10⁻⁴ m² Δ A = A(2α)Δ T = 36×10⁻⁴ × 6.2×10⁻⁵ × 9 ≈ 2.0×10⁻⁶ m² So the answer is (a).

Consider a rectangular sheet of solid material of length l = 9 cm and… | JEE Main 2025 (4 Apr, Shift 2)

Q21JEE Main 2025 · 4 APR · SHIFT 2Medium

Thermometry & Thermal Expansion

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

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Answer: (a)

$\Delta T = \dfrac{Q}{mc} = \dfrac{810}{0.1 \times 900} = 9$ K
$A = 9 \times 4 = 36\text{ cm}^2 = 36\times10^{-4}\text{ m}^2$
$\Delta A = A(2\alpha)\Delta T = 36\times10^{-4} \times 6.2\times10^{-5} \times 9 \approx 2.0\times10^{-6}\text{ m}^2$
So the answer is (a).

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