Answer :
The final temperature of the mixture is -9.1°C.
Principle of a Calorimeter.
Higher body temperatures release heat while lower body temperatures absorb it. The law of conservation of energy is demonstrated by the calorimetric principle, which states that the total amount of heat lost by a hot body is equal to the total amount of heat gained by a cold body.
Here,
Mass of water [tex]m_{w}[/tex] =500g
Mass of ice [tex]m_{i}[/tex] = 100g
Specific heat of water = 1 cal g⁻¹°c⁻¹
Specific heat of ice = 80 °cal g⁻¹
Let T represent the mixture's final temperature.
How much heat water loses
[tex]m_{w} s_{w}[/tex](∆T)w = 500×1(50-T)
Amount of heat that ice absorbs
[tex]m_{i} L_{fi}[/tex]+[tex]m_{i} s_{w}[/tex](∆T)i = 100×80×100×1(T-0)
In accordance with the calorimetry principle:
Heat gained minus Heat Lost
500×1(50-T) = 100×80+100×1(T-0)
500(50-T) = 8000+100T
2500-500T = 8000+100T
2500-8000 = 100T+500T
-5500 =600T
T = -5500/600
T = -9.1°C.
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