Question

How much heat is needed to transform a 1 kg block of ice at $5^{o}C$ to a puddle of water at ${10}^{o}C$?

Answer 1

First, we need to know how much heat it takes to raise the temperature of the ice to 0 C:
$Q=mc\Delta T$
$=\left(1kg\right)(2.20\times {10}^{3}J/kg{\cdot }^{o}C)\left(5^{o}C\right)$
$=1.1\times 0^{4}J$
Next, we need to know how much heat it takes to melt the ice into water:
$Q=m{q}_{fusion}$
$=\left(1kg\right)(3.3\times {10}^{5}J/kg)$
$=3.3\times {10}^{5}J$
Last, we need to know how much heat it takes to warm the water up to 10 C.
Now we just add the three figures together to get our answer:
$1.1\times {10}^4+3.3\times {10}^5+4.2\times {10}^4=3.8\times {10}^6$
Note that far more heat was needed to melt the ice into liquid than was needed to increase the temperature.