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 J^{g–1}; Specific heat capacity of copper = 0.4 Jg^{–1}°C^{–1}] .

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#### Solution

m_{w} =104g

T_{w} = 30° C

m_{c} = 42 g

T =10°C

m_{i} = ?

By Calorimetry,

Heat lost = Heat gained

m_{w} S_{w}(T_{w} -T) + m_{c} S_{c}(T_{w} - T) =m_{i} α + m_{i} S_{w}(T-T_{i})

⇒ (104)(4.2)(30 -10) +(42)(0.4)(30 -10) = m_{i} (336)+ m_{i}(4.2)(10- 0)

⇒ m_{i }`=((104)(4.2)(20)+(42)(0.4)(20))/((336+42)) = 24 g`

Concept: Specific Heat Capacity

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