A rectangular sheet has length 9 cm, width 4 cm, coefficient of linear expansion α = 3.1×10⁻⁵ K⁻¹, mass 0.1 kg and specific heat capacity 900 J kg⁻¹ K⁻¹. If 8.1×10² J of heat is supplied, the increase in its area is:
Options

Question

A rectangular sheet has length 9 cm, width 4 cm, coefficient of linear expansion α = 3.1×10⁻⁵ K⁻¹, mass 0.1 kg and specific heat capacity 900 J kg⁻¹ K⁻¹. If 8.1×10² J of heat is supplied, the increase in its area is:

Options

G1 Physics · Accepted Answer

First find the temperature rise: Q = mcΔT. Thus, ΔT = Q/(mc) = 810/[0.1×900] = 9 K. Initial area: A = (9 cm)(4 cm) = 36 cm² = 36×10⁻⁴ m². For an isotropic solid, the superficial expansion coefficient is approximately 2α. Hence, ΔA = 2αAΔT. Substitute: ΔA = 2(3.1×10⁻⁵)(36×10⁻⁴)(9) ≈ 2.01×10⁻⁶ m². Therefore the nearest listed value is 2.0×10⁻⁶ m². Correct option: B.