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Vikrant Vijayent Lachman
Asked: 2022-11-10T04:59:29+05:30 In:

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)`.

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)`.
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  1. 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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