Question

One end of a copper rod of uniform cross section and length $1.5\text{m}$ is in contact with ice and the other end with steam at ${100}^{\circ }\text{C}$. At what point along its length from $\text{A}$ should a temperature of ${200}^{\circ }\text{C}$ be maintained so that in steady state, the mass of the ice melting is equal to that of steam produced in the same interval of time . $[L_v=540\text{cal/g},L_f=80\text{cal/ g}]$

• A. $10.34\text{cm}$
• B. $9.1\text{cm}$
• C. $20\text{cm}$
• D. $5\text{cm}$

Answer 1

The correct option is A $10.34\text{cm}$

Let $\text{C}$ be the point where ${200}^{\circ }\text{C}$ temperature is maintained.


Heat flow towards the end $\text{A}$ is given by
$H_1=\frac{kA(200-100)}{x}=m\times 540.....\left(1\right)$
where $m$ is rate of steam produced.
Heat flow towards the end $\text{B}$ is given by
$H_2=\frac{kA(200-0)}{150-x}=m^{\prime }\times 80....\left(2\right)$
where $m^{\prime }$ is rate of ice melting.

Given $m=m^{\prime }$
$\therefore$ By dividing $\left(1\right)$ and $\left(2\right)$, we get
$\frac{100(150-x)}{200x}=\frac{540}{80}$
$\Rightarrow 8(150-x)=54\times 2x$
$\Rightarrow 116x=1200$
$\Rightarrow x=10.34\text{cm}$
Thus, option (a) is the correct answer.