We know that the mass of the material is directly proportional to the amount of energy needed. Where #m# is the mass and #q# the energy, we can write:
#qpropm#. Using this, we have two methods to answer the question.
Method 1
#q=mL_f#, where #L_f# is a constant.
What is #L_f#, this constant? It is the specific latent heat of fusion, defined as is the heat needed to change a mass of #1"kg"# the substance from a solid at its melting point into liquid at the same temperature.
So we can write that #L_f=q/m#
Here, #m=0.085"kg"# and #q=8.5xx10^4"J"#. Inputting:
#L_f=(8.5xx10^4)/0.085#
#L_f=1000000"J/kg"#, or #1000"kJ/kg"#
In the second situation, #m=170000"kg"#
We know that #q=mL_f#. We simply input:
#q=170000*1000=170000000"kJ"#, or #170000"MJ"#
Method 2
We know that #qpropm#, and it follows that #q_1/m_1=q_2/m_2#, or:
#q_1m_2=q_2m_1#
We simply input the values needed:
#85*170000=0.085q_2#
#14450000=0.085q_2#
#q_2=14450000/0.085#
#q_2=170000000"kJ"#, or #170000"MJ"#
