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Use the specific heat values to answer the following question.

Which of the following has the smallest heat capacity?

\begin{tabular}{|r|r|}
\hline
Substance & [tex]$C_{p} \left( J / g \cdot{ }^{\circ} C \right)$[/tex] \\
\hline
[tex]$H_2O (l)$[/tex] & 4.18 \\
\hline
[tex]$H_2O (s)$[/tex] & 2.03 \\
\hline
[tex]$H_2O (g)$[/tex] & 2.08 \\
\hline
[tex]$Fe (s)$[/tex] & 0.450 \\
\hline
[tex]$Al (s)$[/tex] & 0.897 \\
\hline
[tex]$Cu (s)$[/tex] & 0.385 \\
\hline
[tex]$Sn (s)$[/tex] & 0.227 \\
\hline
[tex]$Pb (s)$[/tex] & 0.129 \\
\hline
[tex]$Au (s)$[/tex] & 0.129 \\
\hline
[tex]$Hg (l)$[/tex] & 0.140 \\
\hline
\end{tabular}



Answer :

GinnyAnswer
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]

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