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 $



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