To calculate the amount of heat absorbed by a sample of copper as it is melted, the chemist needs to understand the phase change process involved.
Let's break down the options given:
1. [tex]\(\Delta H_{\text{fus}}\)[/tex]: This denotes the heat of fusion. It represents the amount of energy required to change a substance from the solid phase to the liquid phase at its melting point without changing its temperature. This constant is crucial for calculations involving the melting of solids.
2. [tex]\(-\Delta H_{\text{vap}}\)[/tex]: This denotes the negative heat of vaporization. Heat of vaporization ([tex]\(\Delta H_{\text{vap}}\)[/tex]) is the energy required to convert a liquid into a gas at its boiling point. The negative sign indicates the reverse process, condensation. This constant is not relevant for the melting process.
3. [tex]\(\Delta H_{\text{vap}}\)[/tex]: This is the heat of vaporization, the energy needed to change a substance from liquid to gas. While significant for boiling and evaporation, it does not apply to melting.
4. [tex]\(-\Delta H_{\text{tus}}\)[/tex]: This option seems to be a typographical error. Typically, there is no such term as [tex]\(\Delta H_{\text{tus}}\)[/tex] in thermodynamics. Hence, this choice should be disregarded.
For melting copper, the chemist needs the energy needed to shift from solid to liquid state. Thus, the correct constant to use is the heat of fusion:
[tex]\[ \Delta H_{\text{fus}} \][/tex]
Hence, the chemist should use [tex]\(\Delta H_{\text{fus}}\)[/tex] to calculate the amount of heat absorbed by the copper sample as it is melted.
