Properties Of Solids And Liquids Question 588
Question: Three liquids with masses $ m _{1},m _{2},m _{3} $ are thoroughly mixed. If their specific heats are $ c _{1},c _{2},c _{3} $ and their temperatures $ T _{1},T _{2},T _{3} $ respectively, then the temperature of the mixture is
Options:
A) $ \frac{c _{1}T _{1}+c _{2}T _{2}+c _{3}T _{3}}{m _{1}c _{1}+m _{2}c _{2}+m _{3}c _{3}} $
B) $ \frac{m _{1}c _{1}T _{1}+m _{2}c _{2}T _{2}+m _{3}c _{3}T _{3}}{m _{1}c _{1}+m _{2}c _{2}+m _{3}c _{3}} $
C) $ \frac{m _{1}c _{1}T _{1}+m _{2}c _{2}T _{2}+m _{3}c _{3}T _{3}}{m _{1}T _{1}+m _{2}T _{2}+m _{3}T _{3}} $
D) $ \frac{m _{1}T _{1}+m _{2}T _{2}+m _{3}T _{3}}{c _{1}T _{1}+c _{2}T _{2}+c _{3}T _{3}} $
Show Answer
Answer:
Correct Answer: B
Solution:
Let the final temperature be $ T{}^\circ C $ . Total heat supplied by the three liquids in coming down to $ 0{}^\circ C $ = $ m _{1}c _{1}T _{1}+m _{2}c _{2}T _{2}+m _{3}c _{3}T _{3} $ ….. (i) Total heat used by three liquids in raising temperature from $ 0{}^\circ C $ to $ T{}^\circ C $ = $ m _{1}c _{1}T+m _{2}c _{2}T+m _{3}c _{3}T $ …..(ii) By equating (i) and (ii) we get $ (m _{1}c _{1}+m _{2}c _{2}+m _{3}c _{3})T $ = $ m _{1}c _{1}T _{1}+m _{2}c _{2}T _{2}+m _{3}c _{3}T _{3} $
$ \Rightarrow $ $ T=\frac{m _{1}c _{1}T _{1}+m _{2}c _{2}T _{2}+m _{3}c _{3}T _{3}}{m _{1}c _{1}+m _{2}c _{2}+m _{3}c _{3}} $ .
