Question

The resulting temperature when 1kg of ice at 0 degrees Celcius is mixed with 9kg of water at 50 degress Celcius is ----------------------- to the nearest whole number.The specific capacity of water is 4200J/kg/K,the specific latent heat of fusion of ice is 330 000J/kg

A. 24 degreees celcius
B. 37 degreees celcius
C. 46 degreees celcius
D. 56 degreees celcius

Answer 1

Answer on Question #55640-Physics-Mechanics-Relativity

The resulting temperature when 1kg of ice at 0 degrees Celsius is mixed with 9kg of water at 50 degrees Celsius is --- to the nearest whole number. The specific capacity of water is 4200J/kg/K, the specific latent heat of fusion of ice is 330 000J/kg

A. 24 degrees Celsius

B. 37 degrees Celsius

C. 46 degrees Celsius

D. 56 degrees Celsius

Solution

Let the final temperature of the water be $x$ and imagine that there is sufficient energy to melt all the ice so that $x > 0$.

The ice requires 330000 J to melt plus $4200 \cdot x$ to raise the temperature to $x$.

This energy comes from cooling the remainder of the water:

mass · temperature change · specific heat = 9(50 - x)4200;

Hence

$$330000 + 4200 \cdot x = 9(50 - x)4200.$$

Now solve

$$330000 + 4200x = 450 \cdot 4200 - 9x \cdot 4200$$ $$x = \frac{450 \cdot 4200 - 330000}{10 \cdot 4200} = 37{}^{\circ} \mathrm{C}.$$

Answer: B. 37 degrees Celsius.

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