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104g of Water at 30°C is Taken in a Calorimeter Made of Copper of Mass 42 G. When a Certain Mass of Ice at 0°C is Added to It, the Final Steady Temperature of the Mixture After the Ice Has Melted, - Physics

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Numerical

104g of water at 30°C is taken in a calorimeter made of copper of mass 42 g. When a certain mass of ice at 0°C is added to it, the final steady temperature of the mixture after the ice has melted, was found to be 10°C. Find the mass of ice added. [Specific heat capacity of water = 4.2 Jg–1°C–1 ; Specific latent heat of fusion of ice = 336 Jg–1; Specific heat capacity of copper = 0.4 Jg–1°C–1] .

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Solution

mw =104g 
Tw = 30° C
mc = 42 g

T =10°C
 mi = ? 
By Calorimetry,
Heat lost = Heat gained

mw Sw(Tw -T) + mc Sc(Tw - T) =mi α + mi Sw(T-Ti)   

⇒ (104)(4.2)(30 -10) +(42)(0.4)(30 -10) = mi (336)+ mi(4.2)(10- 0)  

⇒ mi `=((104)(4.2)(20)+(42)(0.4)(20))/((336+42)) = 24 g`

Concept: Specific Heat Capacity
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