Question

Ice starts forming in lake with water at 0^0C and when the atmospheric temperature is – 10^0C. If the time taken for 1 cm of ice be 7 hr, then the time taken for the thickness of ice to change from 1 cm to 2 cm is

• A. 7 hrs
• B. 14 hrs
• C. Less than 7 hrs
• D. More than 7 hrs

Answer 1

Answer: (D)

More than 7 hrs

Answer 2

Time required in increment of thickness from y₁ to y­₂

$t = \frac{\rho L}{2K\theta}(y_{2}^{2} - y_{1}^{2})$

In first condition y₁ = 0, y_­2 = 1 cm then ∆t₁ ∝ (1² – 0²)

In second condition y₁ = 1 cm, y₂ = 2 cm then ∆t₂ ∝ (2² – 1²)

∴$\frac{\Delta t_{1}}{\Delta t_{2}} = \frac{1}{3}$ ⇒ ∆ t₂ = 3 × ∆t₁ = 3 × 7 = 21 hrs.