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A metal rod AB of length 10x has its one...

A metal rod AB of length 10x has its one end A in ice at `0^@C`, and the other end B in water at `100^@C`. If a point P one the rod is maintained at `400^@C`, then it is found that equal amounts of water and ice evaporate and melt per unit time. The latent heat of evaporation of water is `540cal//g` and latent heat of melting of ice is `80cal//g`. If the point P is at a distance of `lambdax` from the ice end A, find the value `lambda`. [Neglect any heat loss to the surrounding.]

Text Solution

Verified by Experts

The correct Answer is:
9
`(dm_("ice"))/(dt)=(dm_("vapour"))/(dt)`

`Q_(1)=(KA400)/(t)=mxx80`
ltbr. `Q_(1)=(KA(400-100)t)/((10-lamda)x)t=mxx540`
Dividing both, `lamda=9`
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A metal rod AB of length 10x has it one end in ice at 0^(@)C and the other end B in water at 100^(@)C If a point P on the rod is maintained at 400^(@)C then it is found that equal amounts of water and ice evaporate and melt per unit time. The latent heat of melting of ice is 80cal//g If the point P is at a distance of lambdax from the ice end A find the value of lambda [neglect any heat loss to the surrounding] . .

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Knowledge Check

  • The latent heat of vaporisation of water at 100 ^(@)C is 540 cal g^(-1) . Calculate the entropy increase when one mole of water at 100^(@)C is evaporated

    A
    `26 cal K^(-1) mol^(-1)`
    B
    `1.82 cal K^(-1) mol^(-1)`
    C
    `367 cal K^(-1) mol^(-1)`
    D
    `540xx18 cal K^(-1) mol^(-1)`