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Question

100 g of ice (latent heat 80 cal g1) at 0C is mixed with 100 g of water (specific heat 1 cal g1 C1) at 80C. The final temperature of the mixture will be:

A
0C
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B
40C
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C
80C
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D
<0C
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Solution

The correct option is A 0C
Given that,
Latent heat of fusion of ice (Lf)=80 cal/g
Specific heat capacity of water (cw)=1 cal/gC
Mass of ice (mi)=100 g
Mass of water (mw)=100 g
Initial temperature of ice (T1)=0C
Initial temperature of water (T2)=80C
Let the temperature of mixture be T.

Heat released in melting 100 g of ice to water is: Q1=miLf=100×80=8000 cal
& Heat required to reduce the temperature of water from 80C to 0C is:
Q2=mwcwΔT=100×1×(800)=8000 cal
Q1=Q2
From the priciple of calorimetry, we can say that heat released from the cooling of water at 80 C will be used to just melt the given mass of ice. At equilibrium, temperature of the system will be 0C.
Thus, option (a) is the correct answer.

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