Question

a box made of wood of thickness 2 cm and having dimensions 100cm , 60cm , 60cm contains ice at 0°c . If the temperature outside the box is 30°c and the coefficient of thermal conductivity of wood is 0.0004 CGS unit. then calculate the rate at which ice melt in the box.​

Answer 1

we know, \frac{dQ}{dt}=kA\frac{dT}{dx}

dt

dQ

=kA

dx

dT

where k is thermal conductivity, A is cross sectional area , dT is change in temperature and dx is thickness.

here, k = 0.169w/mK

dT = 35°C = 273 + 35 = 308K

combined area of six faces = 2 x (1 x 0.6 + 0.6 x 0.4 + 0.4 x 1) m² = 2.48 m²

dx = 2.5cm = 0.025m

now, dQ/dt = 0.169 × 2.48 × 308/0.025

= 5,163.5584 J/s or, 1,229.41867Cal/s

hence, rate of melting of ice is 1,229.41867 Cal/s