Properties Of Solids And Liquids Question 541
Question: The temperature of equal masses of three different liquids A, B and C are $ 12{}^\circ C, $
$ 19{}^\circ C $ and $ 28{}^\circ C $ respectively. The temperature when A and B are mixed is $ 16{}^\circ C $ and when B and C are mixed is $ 23{}^\circ C, $ The temperature when A and C are mixed is
Options:
A) $ 18.2{}^\circ C $
B) $ 22{}^\circ C $
C) $ 20.2{}^\circ C $
D) $ 25.2{}^\circ C $
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Answer:
Correct Answer: C
Solution:
Heat gain = heat lost
$ c _{A}( 16-12 )=c _{B}( 19-16 )\Rightarrow \frac{c _{A}}{c _{B}}=\frac{3}{4} $
and $ c _{B}( 23-19 )=c _{C}( 28-23 )\Rightarrow \frac{c _{B}}{c _{C}}=\frac{5}{4} $
$ \Rightarrow \frac{c _{A}}{c _{C}}=\frac{15}{16}………( i ) $
If $ \theta $ is the temperature when A and C are mixed then,
$ c _{A}( \theta\text{ -12} )=c _{C}( 28-\theta )\Rightarrow \frac{c _{A}}{c _{C}}=\frac{28-\theta}{\theta\text{ -12}}…( ii ) $
On solving equations (i) and (ii) $ 9=20.2{}^\circ C $
