# Question #483cf

Dec 7, 2016

91804 J

#### Explanation:

This problem requires you to calculate two heats in order to solve it completely: the heat required to raise the temperature of the ice to its melting point of ${0}^{o} C$, and the heat required to break the intermolecular forces between the molecules to create a liquid.

First, we'll work on raising the temperature to ${0}^{o} C$. This is easily done through the equation:

$q = c m \Delta T$

Where:
$c =$ heat capacity
$m =$ mass (g)
$T =$ temperature

The heat capacity of water is $4.184 \frac{J}{g} ^ o C$ All you need to do now is plug in your given numbers, and find the heat:

$q = \left(4.184\right) \left(200\right) \left(0 - \left(- 30\right)\right)$
$= 25104 J$

Next, we need to find the heat needed to actually melt the ice. To do this, we'll need to multiply the grams of ice we have by the enthalpy of fusion of ice , or the amount of energy you need to melt ice. You may have slightly different values for this based on units and rounding used by your specific book, but the one I will use is the one I got from Wikipedia, which is $333.5 \frac{J}{g}$.

Now, we just multiply the two

$q = 333.5 \left(200\right) = 66700 J$

Now all we need to do is add the two heats procured:

$66700 + 25104 = 91804 J$

Note that this is a positive value. This tells you that you are putting thermal energy into the system, which means that the process of melting ice is endothermic, as we would have expected.

Hope that helped :)