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Thermal Properties of Matter

JEE Main level, single correct, medium

69 of 126

Question 69 of 126

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 :

Show answer and solution

Answer: (D) $23.84^{\circ}C$

When

A&B

are mixed

{m}_{1}{S}_{1}(16-10)={m}_{2}{S}_{2}(20-16)

6{m}_{1}{S}_{1}=4{m}_{2}{S}_{2}.......(1)

When

B&C

are mixed

{m}_{2}{S}_{2}(26-20)={m}_{3}{S}_{3}(30-26)

6{m}_{2}{S}_{2}=4{m}_{3}{S}_{3}...........(2)

From equation

(1)

and

(2)

9{m}_{1}{S}_{1}=4{m}_{3}{S}_{3}

When

A&C

are mixed

{m}_{1}{S}_{1}(T-10)={m}_{3}{S}_{3}(30-T)

T=\dfrac{30{m}_{3}{S}_{3}+10{m}_{1}{S}_{1}}{{m}_{1}{S}_{1}+{m}_{3}{S}_{3}}

T=\dfrac{10\left(3{m}_{3}{S}_{3}+{m}_{1}{S}_{1}\right)}{{m}_{3}{S}_{3}+{m}_{1}{S}_{1}}

T=\dfrac{10\left(3{m}_{3}{S}_{3}+\dfrac{4}{9}{m}_{3}{S}_{3}\right)}{{m}_{3}{S}_{3}+\dfrac{4}{9}{m}_{3}{S}_{3}}

T=\dfrac{10\times 31}{13}

=23.84^{\circ}C

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