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 :

Solution

Physics sir · 3 steps

Heat gives the temperature rise, and then the area grows with twice alpha. Two short steps.

1. Temperature rise. All the heat goes into warming the sheet, so Q = mcΔ T. That gives Δ T = 810/(0.1 × 900) = 810/90 = 9 K.
2. Area coefficient. A sheet expands in two directions, so its area coefficient is β = 2α = 6.2 × 10⁻⁵ K⁻¹. The original area is A = 9 × 4 = 36 cm² = 36 × 10⁻⁴ m².

   Δ A = A (2α) Δ T = 36 × 10⁻⁴ × 6.2 × 10⁻⁵ × 9

3. So. Δ A = 2008.8 × 10⁻⁹ ≈ 2.0 × 10⁻⁶ m², which is option (a).

The idea to keep. For a surface use β = 2α, and for a volume use γ = 3α. When heat is given instead of a temperature change, find Δ T from Q = mcΔ T first.

Answer from the NTA final answer key. Solution by PrepWiser.