Given data:
Mass of copper is,
[tex]m_c=1\text{ kg}[/tex]Initial temperature of copper is,
[tex]T_i=330^oC[/tex]Final temperature of copper is,
[tex]T_f=3300^oC[/tex]Melting point of copper is,
[tex]T_m=1085^oC[/tex]Specific heat capacity of copper is,
[tex]c=389\text{ J/kg}\cdot^oC[/tex]Latent heat of fusion of copper is,
[tex]L_f=206\times10^3\text{ J/kg}[/tex]Boiling point of copper is,
[tex]T_b=2562^oC[/tex]Latent heat of vaporization of copper is,
[tex]\begin{gathered} L_v=322.1\text{ }\times10^3\text{ J/mol} \\ L_v=5069.85\text{ }\times10^3\text{ J/kg} \end{gathered}[/tex]Now,
Formula of heat needed to change the temperature of copper,
[tex]\Delta T=1085^oC-330^oC=755^oC[/tex]Formula:
[tex]Q=mc\Delta T[/tex]Substitute known values in above equation,
[tex]\begin{gathered} Q_1=1\text{ kg}\times389\text{ J/kg}\cdot^oC\times755^oC \\ Q_1=293695\text{ J} \end{gathered}[/tex]Formula for heat needed to melt copper is,
[tex]Q=mL_f[/tex]Substitute known values in above equation,
[tex]\begin{gathered} Q_2=1\text{ kg}\times\times206\times10^3\text{ J/kg} \\ Q_2=206000\text{ J} \end{gathered}[/tex]Formula of heat needed to raise temperature of copper,
[tex]\Delta T=2562^oC-1085^oC=1477^oC[/tex]Formula:
[tex]Q=mc\Delta T[/tex]Substitute known values in above equation,
[tex]\begin{gathered} Q_3=1\text{ kg}\times389\text{ J/kg}\cdot^oC\times^{}1477^oC \\ Q_3=574553\text{ J} \end{gathered}[/tex]Now, formula of heat needed to vaporization of copper is as follows:
[tex]Q_4=mL_v[/tex]Substitiute known values in above equation,
[tex]\begin{gathered} Q_4=1\text{ kg}\times5069.85\times10^3\text{ J/kg} \\ Q_4=5069850\text{ J} \end{gathered}[/tex]Formula of heat needed to change the temperature of copper,
[tex]\Delta T=^{}3300^oC-2562^oC=738^oC[/tex][tex]Q_5=mc\Delta T[/tex]Substitute known values in above equation,
[tex]\begin{gathered} Q_5=1\text{ kg}\times389\text{ J/kg}\cdot^oC\times738^oC \\ Q_5=287082\text{ J} \end{gathered}[/tex]Above diagram is the phase diagram of copper.
