Answer:
At 1825
The value is [tex]\rho_p = 8.9188 \ g/cm^3 [/tex]
At 1965
The value is
The value is [tex]\rho_p = 8.831 \ g/cm^3 [/tex]
At Today
The value is [tex]\rho_p = 8.8755 \ g/cm^3 [/tex]
Explanation:
From the question we are told that
The percentage of copper in 1825 penny is 100%
The percentage of copper in 1860 penny is 88%
The percentage of nickel is 1860 penny is 12%
The percentage of copper in 1965 penny is 95%
The percentage of zinc in 1965 penny is 5%
The percentage of copper in today's penny is 97.5%
The percentage of zinc in today's penny is 2.5%
The density of copper is [tex]\rho_c = 8.92 g/cm^3[/tex]
The density of zinc is [tex]\rho_z = 7.14 g/cm^3[/tex]
The density of nickel is [tex]\rho_n = 8.91 g/cm^3[/tex]
Considering 1825
The density of penny is [tex]\rho_p = 8.92 g/cm^3[/tex] because the penny was made up of 100% copper
Considering 1860
Generally the density of penny is mathematically evaluated as
[tex]\rho_p = [\frac{88}{100} * \rho_c] +[\frac{12}{100} * \rho_z][/tex]
=> [tex]\rho_p = [\frac{88}{100} * 8.92 ] +[\frac{12}{100} * 8.91 ][/tex]
=> [tex]\rho_p = 8.9188 \ g/cm^3 [/tex]
Considering 1965
Generally the density of penny is mathematically evaluated as
[tex]\rho_p = [\frac{95}{100} * \rho_c] +[\frac{5}{100} * \rho_n][/tex]
=> [tex]\rho_p = [\frac{95}{100} * 8.92 ] +[\frac{5}{100} * 7.14 ][/tex]
=> [tex]\rho_p = 8.831 \ g/cm^3 [/tex]
Considering today
Generally the density of penny is mathematically evaluated as
[tex]\rho_p = [\frac{97.5}{100} * \rho_c] +[\frac{2.5}{100} * \rho_z][/tex]
=> [tex]\rho_p = [\frac{97.5}{100} * 8.92 ] +[\frac{2.5}{100} * 7.14 ][/tex]
=> [tex]\rho_p = 8.8755 \ g/cm^3 [/tex]
