Question

Two identical metal plates are welded end to end as shown in Fig. (i). $20cal$ of heat flows through it in $4$ minutes. If the plates are welded as shown in Fig. (ii), find the time (in minutes) taken by the same amount of heat to flow through the plates.

Answer 1

Answer: 6

$V_1\to$ Initial volume of vessel
$V_2\to$ Initial volume of $Hg$

Given $V_1-V_2=34$
Let temperature is increased by $\Delta T$, then
$V_1^{\prime }-V_2^{\prime }=34\to$ as volume of unfilled part remains same. .....(i)
$\Rightarrow V_1[1+3\alpha \Delta T]-V_2[1+\gamma \Delta T]=34$
$\Rightarrow 3V_1\alpha =V_2\gamma$.....(ii)
From (i) and (ii), $V_2=6c{m}^3$