To determine which substance has the smallest specific heat capacity, we need to compare the given specific heat values for each substance.
Let's list the specific heat capacities:
1. [tex]\(H_2O (l)\)[/tex]: 4.18 [tex]\(J/(g \cdot °C)\)[/tex]
2. [tex]\(H_2O (s)\)[/tex]: 2.03 [tex]\(J/(g \cdot °C)\)[/tex]
3. [tex]\(H_2O (g)\)[/tex]: 2.08 [tex]\(J/(g \cdot °C)\)[/tex]
4. [tex]\(Fe (s)\)[/tex]: 0.450 [tex]\(J/(g \cdot °C)\)[/tex]
5. [tex]\(Al (s)\)[/tex]: 0.897 [tex]\(J/(g \cdot °C)\)[/tex]
6. [tex]\(Cu (s)\)[/tex]: 0.385 [tex]\(J/(g \cdot °C)\)[/tex]
7. [tex]\(Sn (s)\)[/tex]: 0.227 [tex]\(J/(g \cdot °C)\)[/tex]
8. [tex]\(Pb (s)\)[/tex]: 0.129 [tex]\(J/(g \cdot °C)\)[/tex]
9. [tex]\(Au (s)\)[/tex]: 0.129 [tex]\(J/(g \cdot °C)\)[/tex]
10. [tex]\(Hg (l)\)[/tex]: 0.140 [tex]\(J/(g \cdot °C)\)[/tex]
Next, identify the smallest value among these specific heats:
- [tex]\(0.129\)[/tex] [tex]\(J/(g \cdot °C)\)[/tex]
We observe that the specific heat capacity value of 0.129 [tex]\(J/(g \cdot °C)\)[/tex] is shared by two substances:
- [tex]\(Pb (s)\)[/tex] (Lead solid)
- [tex]\(Au (s)\)[/tex] (Gold solid)
Therefore, the substances with the smallest specific heat capacity are:
[tex]\[
\boxed{Pb (s) \, \text{and} \, Au (s)}
\][/tex]
