A substance of mass $m\, kg$ requires a power input of $P$ watts to remain in the molten state at its melting point. When the power is turned off, the sample completely solidifies in time $t$ sec. What is the latent heat of fusion of the substance

  • [IIT 1992]
  • A

    $\frac{{Pm}}{t}$

  • B

    $\frac{{Pt}}{m}$

  • C

    $\frac{m}{{Pt}}$

  • D

    $\frac{t}{{Pm}}$

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Values for latent heat in Column$-\,I$ and its values are given in Column$-\,II$. Match the followings :

Column $-\,I$ Column $-\,II$
$(a)$ Latent heat of vaporization $L_V$ $(i)$ $22.6\, \times \,{10^5}\,J\,/kg$
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    $(iii)$ $3.33\, \times \,{10^5}\,J\,/kg$

A metal rod $\mathrm{AB}$ of length $10 x$ has its one end $\mathrm{A}$ in ice at $0^{\circ} \mathrm{C}$ and the other end $\mathrm{B}$ in water at $100^{\circ} \mathrm{C}$. If a point $\mathrm{P}$ on the rod is maintained at $400^{\circ} \mathrm{C}$, 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 $540 \ \mathrm{cal} / \mathrm{g}$ and latent heat of melting of ice is $80 \ \mathrm{cal} / \mathrm{g}$. If the point $\mathrm{P}$ is at a distance of $\lambda x$ from the ice end $\mathrm{A}$, find the value of $\lambda$.

[Neglect any heat loss to the surrounding.|

  • [IIT 2009]

By exerting a certain amountof pressure on an ice block, you

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