Solveeit Logo
Login

Question

Question: On a cold winter day, the temperature of atmosphere is –TŗC. The cylindrical diagram shown is made o...

On a cold winter day, the temperature of atmosphere is –TŗC. The cylindrical diagram shown is made of insulating material and it contains water at 0ŗC. If L is latent heat of fusion of ice, &r is density of ice and K is thermal conductivity of ice, the time taken for total mass of water to freeze is –

A

ρLH2KT\frac{\rho L}{H^{2}KT}

B

ρLH22KT\frac{\rho LH^{2}}{2KT}

C

ρLH2KT\frac{\rho LH^{2}}{KT}

D

H2ρLKT\frac{H^{2}}{\rho LKT}

Answer

ρLH22KT\frac{\rho LH^{2}}{2KT}

Explanation

Solution

A × dx × r × L = TKAdtx\frac{TKAdt}{x}

∫0Hxdx\int_{0}^{H}{xdx}= ∫0tTKAA×ρdt\int_{0}^{t}{\frac{TKA}{A \times \rho}dt}

H22\frac{H^{2}}{2}= TKtρL\frac{TKt}{\rho L}

t = H2ρL2TK\frac{H^{2}\rho L}{2TK}