1.

A metal rod of length 20 cm and diamter 2 cm is convered with a non conducting substance. One of its ends is maintained at `100^(@)C` , while the other end is put at `0^(@)C`. It is found that 25 g ice melts in 5 min. calculate the coefficient of thermal conductivity of the metal. Latent that of ice = `80 cal g^(-1)`.

Answer» Here, length of the rod,
`Delta x = 20 cpm = 20 xx 10^(-2)m`,
Diameter = 2cm
radius `= r = 1 cm =10^(-2) m`,
Area of cross section
`A = pi r^(2) = pi (10^(-2))^(2) = 10^(-4) pi sq. m,`
`Delta T = 100 - 0 = 100^(@)C`,
Mass of ice melted , `m= 25 g , L = 80 cal.g^(-1)`
`:.` Heat conducted,
`Delta Q = m L = 25 xx 80 = 2000 cal.`
`= 2000 xx 4.2 J`
`Delta t = 5 min = 300 s`
As, `(Delta Q)/(Delta t) =( KA (Delta T))/(Delta x)`
`:. K = (Delta Q//Delta t)/(A Delta T//Delta x) = (Delta Q Delta x)/(Delta t.A Delta T)`
`=(2000 xx 4.2 xx 20 xx 10^(-2))/(300 xx 10^(-4)pi xx 100)`
`=1.78 Js^(-1)m^(-1) .^(@)C^(-1)`.


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