Question

Two identical metal plates are welded end to end as shown in Fig. (i). $20 \,cal$ 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

$V_{1} \rightarrow$ Initial volume of vessel
$V_{2} \rightarrow$ Initial volume of $Hg$

Given $V_{1}-V_{2}=34$
Let temperature is increased by $\Delta T$, then
$V_{1}^{\prime}-V_{2}^{\prime}=34 \rightarrow$ as volume of unfilled part remains same. .....(i)
$\Rightarrow V_{1}[1+3 \alpha \Delta T]-V_{2}[1+\gamma \Delta T]=34 $
$\Rightarrow 3 V_{1} \alpha=V_{2} \gamma$.....(ii)
From (i) and (ii), $V_{2}=6 \,cm ^{3}$