Question

One end of a metal rod of uniform cross-section and length $1.5$ m is in contact with ice at one end and the other end is in contact with steam at ${100}^o$C. At what point along its length should a temperature of ${200}^o$C be maintained so that in the steady state the mass of ice melting is equal to that of steam produced in the same interval of time? (Specific latent heat of ice = $80$ kcal kg${}^{-1}$ and that of steam = $540$ kcal kg${}^{-1}$

• A. 1.4 m from cold end
• B. 0.104 m from cold end
• C. 1.52 m from cold end
• D. 0.15 m from cold end

Answer 1

The correct option is A 1.4 m from cold end

Let x be the required distance from cold end.
$80\times {10}^3\times m=\frac{\lambda A(200-0)}{\times }$
Where m is the mass of ice melted in one second which is equal to mass of steam formed in one second
$540\times {10}^3\times m==\frac{\lambda A(200-100)}{(1.5-\times )}$
$\frac{80}{540}=\frac{200(1.5-x)}{100x}$
$\therefore x=1.4m$