The correct option is D 21 hours
Let us assume that x length of ice has formed and to form a small strip of ice of length dx, dt time is required, then dQdt=KAΔ Tx
d(mL)dt=KAΔ Tx
AρwLdxdt=KAΔ Tx
dt=ρxLxdxKΔ T
where,
K is thermal conductivity of ice,
A is area of the lake,
L is talent heat of ice,
ρw are mass density of ice and
Δ T is the temperature difference.
By integrating the above equation on both, sides
∫t0dt=ρwLKΔ T∫l0xdx
t=ρwLKΔ Tl22
t=Cl22
where C=ρwLKΔ T
Given that to form ice of 1 cm thickness, time of 7 hours has been taken then, time required to form 2 cm thickness of ice will be given by
t1l21=t2l22
t2=t1l21l22=71×4 =28 hours
Time taken to increase thickness of ice from 1 cm to 2 cm is t2−t1=28−7=21 hours