Ice starts forming in a lake where the water is at 0 ° C and the...

If at some time& $t$, the thickness of ice is& x and at time&t + dt$, the thickeness is$x + dx$, then</p><p>\left(ρAdx\right){L}_{fusion} = \dfrac{kA\left(0 - \left(-10\right)\right)}{x}dt$

$⇒ ∆ t = \dfrac{ρ{L}_{fusion}}{20k}\left({x}_{2}^{2} - {x}_{1}^{2}\right)</p><p>$⇒ ∆ t ∝ ( {x}_{2}^{2} - {x}_{1}^{2} )$</p><p>$⇒ $\dfrac{∆ t}{∆ t '} = \dfrac{{x}_{2}^{2} - {x}_{1}^{2}}{\left(x{'}_{2}\right)2 - \left(x{'}_{1}\right)2}</p><p>$⇒ $\dfrac{7}{∆ t '} = \dfrac{( {1}^{2} - {0}^{2} )}{( {2}^{2} - {1}^{2} )}</p><p>$⇒ ∆ t ' = 21hours$</p>$