Two Experimental Runs Are Performed to Determine the Calorimetric Properties $- 10.0 ^ { \circ } \mathrm { C } .$

Two experimental runs are performed to determine the calorimetric properties of an alcohol which
has a melting point of $- 10.0 ^ { \circ } \mathrm { C } .$ In the first run, a 200-g cube of frozen alcohol, at the melting point,
is added to 300 g of water at $20.0 ^ { \circ } \mathrm { C }$ in a styrofoam container. When thermal equilibrium is
reached, the alcohol-water solution is at a temperature of $5.0 ^ { \circ } \mathrm { C }$ In the second run, an identical
cube of alcohol is added to 500 g of water at $20.0 ^ { \circ } \mathrm { C }$ and the temperature at thermal equilibrium is
$10.0 ^ { \circ } \mathrm { C }$ The specific heat capacity of water is $4190 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K } .$ Assume no heat is exchanged with the
styrofoam container and the surroundings. What is the heat of fusion of the alcohol?

A) $8.7 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$
B) $7.9 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$
C) $7.1 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$
D) $6.3 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$
E) $5.5 \times 10 ^ { 4 } \mathrm {~J} / \mathrm { kg }$