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

(A) $2.0 \times 10^{-6} \mathrm{~m}^{2}$

(B) $3.0 \times 10^{-7} \mathrm{~m}^{2}$

(C) $6.0 \times 10^{-7} \mathrm{~m}^{2}$

(D) $4.0 \times 10^{-7} \mathrm{~m}^{2}$

JEE Main · 2025 · 04 Apr 2025 · Shift 2 · Heat & Thermodynamics

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 kg^{- 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 :-

Answer: (A)

The supplied heat raises the temperature through

Δ Q = m C_{v} Δ T

, giving

Δ T = \frac{8.1 \times 1 0 ^{2}}{0.1 \times 900} = 9

K. The original area is

A_{0} = 9 \times 4 = 36 cm^{2} = 36 \times 1 0^{- 4} m^{2}

, and an area expands with twice the coefficient of linear expansion,

Δ A = A_{0} (2 α) Δ T

. Substituting,

Δ A = 36 \times 1 0^{- 4} \times 2 \times 3.1 \times 1 0^{- 5} \times 9 = 2.0 \times 1 0^{- 6} m^{2}

JEE Main · 2025 · 04 Apr 2025 · Shift 2 · Single correct option