Question

The temperature of equal masses of three different liquids $x,y$ and $z$ are $10^{\circ }C,20^{\circ }C$ and $30^{\circ }C$ respectively. The temperature of mixture when $x$ is mixed with $y$ is $16^{\circ }C$ and that when $y$ is mixed with $z$ is $26^{\circ }C$. The temperature of mixture when $x$ and $z$ are mixed will be:

• A. $28.32^{\circ }C$
• B. $25.62^{\circ }C$
• C. $23.84^{\circ }C$
• D. $20.28^{\circ }C$

Answer 1

Answer: (C)

X	Y	Z
$m_1=m$	$m_2=m$	$m_3=m$
$T_1=10^{\circ }C$	$T_2=20^{\circ }C$	$T_3=30^{\circ }C$
$s_1$	$s_2$	$S_3$

when $x\&y$ are mixed, $T_{f_1}=16^{\circ }C$
$m_1{s}_{1}T+m_2{s}_2{T}_2$
$=\left(m_1{s}_1+m_2{s}_2\right)T{f}_1$
$s_1\times 10+s_2\times 20$
$=\left(s_1+s_2\right)\times 16$
$s_1=\frac{2}{3}{s}_2\dots .(i)$
when $y\&z$ are mixex, $T_{f_2}=26^{\circ }C$
$m_2{s}_{2}T+m_3{s}_3{T}_3$
$=\left(m_3{s}_3+m_3{s}_3\right)T{f}_2$
$s_2\times 20+s_3\times 30$
$=\left(s_2+s_3\right)\times 26$
$s_3=\frac{3}{2}{s}_2\dots ..(ii)$
when $x\&z$ are mixex
$m_1{s}_1{T}_1+m_3{s}_3{T}_3$
$=\left(m_1{s}_1+m_3{s}_3\right)Tf$
$\frac{2}{3}{s}_2\times 10+\frac{2}{3}{s}_2\times 20$
$=\left(\frac{2}{3}{s}_2+\frac{3}{2}{s}_2\right)T_f$
$T_f=23.84{}^{\circ }C$