Ice starts forming in a lake where the water is at 0 ° C and the ambient temperature is - 1 0 ° C . If the time taken for 1 c m of ice to be formed is 7 hours , then the time taken for the thickness of ice to change from 1 c m to 2 c m is

Step-by-step solution

If at some time t , the thickness of ice is x and at time t + dt , the thickeness is x + dx , then ρAdx L fusion = kA 0 - - 10 x dt ⇒ ∆ t = ρ L fusion 20 k x 2 2 - x 1 2 ⇒ ∆ t ∝ ( x 2 2 - x 1 2 ) ⇒ ∆ t ∆ t ' = x 2 2 - x 1 2 x ' 2 2 - x ' 1 2 ⇒ 7 ∆ t ' = ( 1 2 - 0 2 ) ( 2 2 - 1 2 ) ⇒ ∆ t ' = 21 hours