<u>Answer:</u> The amount of heat needed to melt the ice cube is 6.083 kJ
<u>Explanation:</u>
The processes involved in the given problem are:

To calculate the amount of heat required to melt the ice at its melting point, we use the equation:

where,
= amount of heat absorbed = ?
m = mass of ice = 10.000 g
= enthalpy change for fusion = 334.16 J/g
Putting all the values in above equation, we get:

To calculate the heat required at different temperature, we use the equation:

where,
= heat absorbed
m = mass of ice = 10.000 g
c = specific heat capacity of water = 4.184 J/g.°C
= change in temperature = ![T_2-T_1=[65.0-0]^oC=65.5^oC](https://tex.z-dn.net/?f=T_2-T_1%3D%5B65.0-0%5D%5EoC%3D65.5%5EoC)
Putting values in above equation, we get:

Total heat absorbed = 
Total heat absorbed = ![[3341.6+2741.83]J=6083.43J=6.083kJ](https://tex.z-dn.net/?f=%5B3341.6%2B2741.83%5DJ%3D6083.43J%3D6.083kJ)
Hence, the amount of heat needed to melt the ice cube is 6.083 kJ