Question

Calculate the velocity with which a piece on ice at $-5^{o}C$ be thrown against a wall so that its entire mass melts upon contact. Latent heat of $ice=80cal{g}^{-1},$ specific heat of $ice=0.5cal{g}^{-1}$ ${}^o{C}^{-1}$ and $J=4.2\times {10}^{7}ergca{l}^{-1}$

• A. $700m{s}^{-1}$
• B. $432m{s}^{-1}$
• C. $832.5m{s}^{-1}$
• D. $564m{s}^{-1}$

Answer 1

The correct option is C $832.5m{s}^{-1}$

Given : Calculate the velocity with which a piece on ice at −5oC−5oC be thrown against a wall so that its entire mass melts upon contact.

Latent heat of fusion = $80cal{g}^{-}1$, specific heat of ice =$0.5cal{g}^{-1}$, and J=$4.2\times {10}^7$

Solution :

First we will convert all of them in SI units

Latent heat of ice ${}^{\prime }{L}^{\prime }=80\times 4.2\times {10}^3$=$336\times {10}^3$

specific heat of ice ${}^{\prime }{c}^{\prime }=0.5\times 4.2\times {10}^3$ = $2.1\times {10}^3$

Kinetic Energy= total energy to melt ice

$\frac{1}{2}m{v}^2=mC\Delta T+mL$

$\frac{1}{2}{v}^2=C\Delta T+L$

$v^2=2(2.1\times {10}^3+\times 5+336\times {10}^3)$

$v=832.5m{s}^{-1}$

The Correct Opt=C