Answer: The amount of heat needed to melt the ice cube is 6.083 kJ
Explanation:
The processes involved in the given problem are:
[tex]1.)H_2O(s)(0^oC,273K)\rightarrow H_2O(l)(0^oC,273K)\\2.)H_2O(l)(0^oC,273K)\rightarrow H_2O(l)(65.5^oC,338.5K)[/tex]
To calculate the amount of heat required to melt the ice at its melting point, we use the equation:
[tex]q_1=m\times \Delta H_{fusion}[/tex]
where,
[tex]q_1[/tex] = amount of heat absorbed = ?
m = mass of ice = 10.000 g
[tex]\Delta H_{fusion}[/tex] = enthalpy change for fusion = 334.16 J/g
Putting all the values in above equation, we get:
[tex]q_1=10.000g\times 334.16J/g=3341.6J[/tex]
To calculate the heat required at different temperature, we use the equation:
[tex]q_2=mc\Delta T[/tex]
where,
[tex]q_2[/tex] = heat absorbed
m = mass of ice = 10.000 g
c = specific heat capacity of water = 4.184 J/g.°C
[tex]\Delta T[/tex] = change in temperature = [tex]T_2-T_1=[65.0-0]^oC=65.5^oC[/tex]
Putting values in above equation, we get:
[tex]q_2=10.000g\times 4.184J/g.^oC\times 65.5^oC\\\\q_2=2741.83J[/tex]
Total heat absorbed = [tex]q_1+q_2[/tex]
Total heat absorbed = [tex][3341.6+2741.83]J=6083.43J=6.083kJ[/tex]
Hence, the amount of heat needed to melt the ice cube is 6.083 kJ
