Question

# two vessels of different materials are identical in size and wall thickness.they are filled with equal quantities of ice at 0 degree celcius.If the ice completely melts in 10 and 25 min respectively,compare the coefficients of thermal conductivities of the materials of the vessels?

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Solution

## Let the vessels be cubic of side a and thickness be dt1 = 10 mint2 = 25 minLet the room temperature be ToThermal conductivities of the first and the second vessel be K1 and K2 respectivelyLet ∆Q amount of heat is required to melt the volume of ice.∆Q = 6K1a2(To – 0)t1/d(factor of 6 is for the 6 sides of a cube through which heat is flowing in)=> ∆Q = 6K1a2(To – 0)10/d ---1. For the second container∆Q = 6K2a2(To – 0)25/d ---2.From 1 and 26K1a2(To – 0)10/d = 6K2a2(To – 0)25/d=> 10K1 = 25K2=> K1:K2 = 25:10 = 5:2Thus ratio of their thermal conductivity are 5:2

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