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

Answer

D

Explanation

Given ,
Total wall area ( in cluding the lid ) (A ) `= 1.0 cm ^2`
Thickness of wall (l) = `3 cm = 3xx10 ^(-2) m`
Average temperature outside the box `= 30 ^(@) C `
` Delta theta = 30-0= 30 ^(@ ) C `
`L_("fusion (ice )" =3xx10 ^5 j // Kg `
` K_("themocal ") =0.03 W//mK`
we know that ,
` ( Q ) /(t) =(KA)/(I) Delta theta `
For one day , T = 24 `xx 60xx60 s `
` ( m xx L _( " fusion (ice) " ))/(t) = (KA ) /(l) Delta Q `
` ( m xx3xx10 ^5)/(24xx60xx60 ) =( 0.03 xx1 ) /( 3xx10 ^(-2))xx30 `
` m= ( 0.03xx1xx30xx24xx60xx60)/( 3xx 10 ^(-2) xx 3xx10 ^(5))`
` m =(77760)/(9000 )=8.64 Kg `