A) \[31.2{}^\circ C\]
B) \[32.8{}^\circ C\]
C) \[36.7{}^\circ C\]
D) \[38.2{}^\circ C\]
Correct Answer: D
Solution :
Key Idea: According to principle of calorimetry, heat given = heat taken. Let heat given by water to cool upto \[0{{\,}^{o}}C=mc\Delta \theta \]where m is mass, c is specific heat and \[\Delta \theta \]is temperature difference. Heat taken by ice to melt = mL where L is latent heat. Also if \[\theta \] is the temperature of the mixture, then Heat taken = Heat given \[mc\Delta \theta =mL+mc\Delta \theta '\] \[100\times 1\times (50-\theta )=10\times 80+10\times 1\times (\theta -0)\] \[\Rightarrow \]\[500-10\theta =80+\theta \] \[\Rightarrow \]\[11\theta =420\] \[\Rightarrow \]\[\theta =\frac{420}{11}=38.2{{\,}^{o}}C\]
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