Properties Of Solids And Liquids Question 21
Question: 540 g of ice at 0°C is mixed with 540 g of water at 80°C. The final temperature of the mixture is [AFMC 1994]
Options:
A) 0°C
B) 40°C
C) 80°C
D) Less than 0°C
Show Answer
Answer:
Correct Answer: A
Solution:
Heat taken by ice to melt at 0°C is $ Q _{1}=mL=540\times 80=43200cal $
Heat given by water to cool upto 0°C is $ Q _{2}=ms\Delta \theta =540\times 1\times (80-0)=43200cal $
Hence heat given by water is just sufficient to melt the whole ice and final temperature of mixture is 0°C.
Short trick : For these type of frequently asked questions you can remember the following formula $ {\theta _{\text{mix}}}=\frac{m _{W}{\theta _{W}}-\frac{m _{i}L _{i}}{c _{W}}}{m _{i}+m _{W}} $
(See theory for more details) If $ m _{W}=m _{i} $
then $ {\theta _{mix}}=\frac{{\theta _{W}}-\frac{L _{i}}{c _{W}}}{2}=\frac{80-\frac{80}{1}}{2}=0{}^\circ C $
