Bottom of a lake is at 0° C and atmospheric temperature is -20° C. If 1 cm ice is formed on the surface in 24 h, then time taken to form next 1 cm of ice is

Question

Bottom of a lake is at 0° C and atmospheric temperature is -20° C. If 1 cm ice is formed on the surface in 24 h, then time taken to form next 1 cm of ice is (A) 24 h (B) 72 h (C) 48 h (D) 96 h

Tardigrade Admin · Accepted Answer

Time intervals to change thickness from 0 to x from x to 2 x are in ratio of 1: 3: 5: 7 ldots ldots ∴ t1: t2=1: 3 =24: 24 × 3 ⇒ t2=72 hours

Q. Bottom of a lake is at $0^{\circ} C$ and atmospheric temperature is $- 2 0^{\circ} C$ . If $1 c m$ ice is formed on the surface in $24 h$ , then time taken to form next $1 c m$ of ice is

24 h

72 h

48 h

96 h

Time intervals to change thickness from 0 to $x$ from $x$ to $2 x$ are in ratio of $1 : 3 : 5 : 7 \dots\dots$
$∴ t_{1} : t_{2} = 1 : 3$
$= 24 : 24 \times 3$
$\Rightarrow t_{2} = 72$ hours

Q. Bottom of a lake is at 0∘C and atmospheric temperature is −20∘C. If 1cm ice is formed on the surface in 24h, then time taken to form next 1cm of ice is