Question

A copper cylinder has a radius of 2.5 cm and a length of 5.6 cm at 20 degree Celsius. The rod is heated until its temperature is 85 degree Celsius. Find the density of the copper at 85 degree Celsius. If the density of the copper at 20 degree Celsius is 8,960 kg/m^3

Answer 1

Solution.

$r=0.025m;$

$L=0.056m;$

$T=20^OC;$

$\rho=8960kg/m^3;$

$T_1=85^oC;$

$m=V\rho;$

$V=SL=\pi r^2L;$

$V=3.14\sdot0.025^2\sdot0.056=1.1\sdot10^{-4}m^3;$

$m=1.1\sdot10^{-4}\sdot8960=0.9856kg;$

$V_1=V(1+\beta\Delta T);$

$V_1=1.1\sdot10^{-4}(1+5.1\sdot10^{-6}\sdot65)=1.1004\sdot10^{-4}m^3;$

$\rho_1=\dfrac{m}{V_1};$

$\rho_1=\dfrac{0.9856}{1.1004\sdot 10^{-4}}=8956kg/m^3;$

Answer:$\rho_1=8956 kg/m^3.$