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?
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?
Let the vessels be cubic of side a and thickness be d
t1 = 10 min
t2 = 25 min
Let the room temperature be To
Thermal conductivities of the first and the second vessel be K1 and K2 respectively
Let ∆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 2
6K1a2(To – 0)10/d = 6K2a2(To – 0)25/d
=> 10K1 = 25K2
=> K1:K2 = 25:10 = 5:2
Thus ratio of their thermal conductivity are 5:2
Let the vessels be cubic of side a and thickness be d
t1 = 10 min
t2 = 25 min
Let the room temperature be To
Thermal conductivities of the first and the second vessel be K1 and K2 respectively
Let ∆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 2
6K1a2(To – 0)10/d = 6K2a2(To – 0)25/d
=> 10K1 = 25K2
=> K1:K2 = 25:10 = 5:2
Thus ratio of their thermal conductivity are 5:2
