Properties Of Solids And Liquids Question 449
Question: The tempertaure 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:
[c] 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 -12)=C _{C}(28-\theta ) $
$ \Rightarrow \frac{C _{A}}{C _{C}}=\frac{28-\theta }{\theta -12} $ -(ii) On solving equations (i) and (ii) $ \theta = 20.2{}^\circ C $
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