91影视

We can see that the entropy of an ideal gas is $Nk$times a logarithm, and that the entropy of an Einstein solid is likewise $Nk$times a logarithm. Because $N$is a high number for any macroscopic item and the logarithm is considerably smaller, we may ignore the log part and choose $S~Nk$for an approximate order-of-magnitude estimate of the entropy. Here are a few examples of such estimates:

Taking $1kg$of carbon with molar mass of $12脳{10}^{鈭�3}\mathrm{kg}脳{\mathrm{mol}}^{鈭�1}$for $1kg$of book,the number of molecule is

$$\begin{gathered} N=Numberofatomsinonemole脳Numberofmoles \\ N=Numberofatomsinonemole脳\frac{Mass}{Molarmass} \\ N=6.022脳{10}^{23}脳\frac{1}{12脳{10}^{鈭�3}} \\ N=5.018脳{10}^{25}. \end{gathered}$$

Entropy as

$S~Nk$

Substituting $k=1.38脳{10}^{鈭�23}\mathrm{J}脳{\mathrm{K}}^{鈭�1}$,so the entropy of book as

$\begin{array}{l}S~5.018脳{10}^{25}脳1.38脳{10}^{鈭�23}\\ S~692.484\mathrm{J}脳{\mathrm{K}}^{鈭�1}\end{array}$

For a $400kg$of mooses,the approximate of $400kg$of water with molar mass of $18脳{10}^{鈭�3}\mathrm{kg}脳{\mathrm{mol}}^{鈭�1}$,the number of molecules is

$$\begin{gathered} N=6.022脳{10}^{23}脳\frac{400}{18脳{10}^{鈭�3}} \\ N=1.338脳{10}^{28} \end{gathered}$$

The entropy mooses is

role="math" localid="1650273675935" $$\begin{gathered} S~Nk \\ S~1.338脳{10}^{28}脳1.38脳{10}^{鈭�23} \\ S=184644\mathrm{J}脳{\mathrm{K}}^{鈭�1}. \end{gathered}$$

For sun,the ionized hydrogen of $2脳{10}^{30}\mathrm{kg}$with molar mass is${10}^{鈭�3}\mathrm{kg}脳{\mathrm{mol}}^{鈭�1}$ ,the number of molecules is

$$\begin{gathered} N=6.022脳{10}^{23}脳\frac{2脳{10}^{30}}{{10}^{鈭�3}} \\ N=1.2044脳{10}^{57} \end{gathered}$$

The entropy is

$$\begin{gathered} S~1.2044脳{10}^{57}脳1.38脳{10}^{鈭�23} \\ S=1.662脳{10}^{34}\mathrm{J}脳{\mathrm{K}}^{鈭�1}. \end{gathered}$$