Two Experimental Runs Are Performed to Determine the Calorimetric Properties $- 10 ^ { \circ } \mathrm { C }$

Multiple Choice

Two experimental runs are performed to determine the calorimetric properties of an alcohol which has a melting point of $- 10 ^ { \circ } \mathrm { C }$ In the first run, a 200-g cube of frozen alcohol, at the melting point, is added to 300 g of water at $20 ^ { \circ } \mathrm { C }$ in a styrofoam container. When thermal equilibrium is reached, the alcohol-water solution is at a temperature of $5 ^ { \circ } \mathrm { C }$ In the second run, an identical cube of alcohol is added to 500 g of water at $20 ^ { \circ } \mathrm { C }$ and the temperature at thermal equilibrium is $10 ^ { \circ } \mathrm { C }$ 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 specific heat capacity of the alcohol?

A) $1700 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$
B) $2500 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$
C) $2100 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$
D) $2300 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$
E) $1900 \mathrm {~J} / \mathrm { kg } \cdot \mathrm { K }$