A thermocal box has a total wall area ( including the lid ) of 1.0 `m^2` and well thickness of 3 cm . It is filled with ice at `0 ^(@) C ` . If the average temperature outside the box is `30 ^@ C` throughout the day , the amount of ice that melts in one day is
[ Use `K _("themocal " ) = 0.03` W/mk ,
`L _(" Fusion ( ice)")`=`3.00xx 10 ^5 j // KG ]`

Options

A. 1 kg
B. 2.88 kg
C. 25.92 kg
D. 8.64 kg

Answer

D

Explanation

Answer(4) amount of ice melts in one day, m = Q/L
Quantity of heat transferred, `Q = tKA(T_h - T_c)/l` K_thermocol = 0.03 W/m K .
Area, `A = 1m^2` .
Thickness, l = 3cm = `3 xx 10^-2 m`.
`[T_h - T_c] = 30^@C - 0^@C = 30^@C` .
t = `24 xx 60 xx 60 = 86,400 sec` .
`Rightarrow Q = (86400 xx 0.03 xx 1 xx 30)/(3 xx 10^-2)` .
`therefore Q = 2.592 xx 10^6` .
Mass of ice melted, m= Q/Latent fusion of ice .
= `(2.592 xx 10^6) / (3 xx 10^5)` = m = 8.64 kg