Respuesta :
Answer:
[tex]{\rho_{143\ ^0C}}=1.118\times 10^4\ kg/m^3}[/tex]
Explanation:
The expression for the volume expansion is:-
[tex]V_2=V_1\times [1+3\times \alpha\times \Delta T][/tex]
Where,
[tex]V_2\ and\ V_1[/tex] are the volume values
[tex]\alpha[/tex] is the coefficient of linear expansion = [tex]29\times 10^{-6}\ (^0C)^{-1}[/tex]
Also,
Density is defined as:-
[tex]\rho=\frac{Mass}{Volume}[/tex]
or,
[tex]Volume=\frac{Mass}{\rho}[/tex]
Applying in the above equation, we get that:-
[tex]\frac{M}{\rho_2}=\frac{M}{\rho_1}\times [1+3\times \alpha\times \Delta T][/tex]
Or,
[tex]{\rho_2}=\frac{\rho_1}{[1+3\times \alpha\times \Delta T]}[/tex]
So, From the question,
[tex]\Delta T=143-20\ ^0C=123\ ^0C[/tex]
[tex]\rho_1=1.13\times 10^4\ kg/m^3[/tex]
Thus,
[tex]{\rho_2}=\frac{1.13\times 10^4\ kg/m^3}{[1+3\times (29\times 10^{-6}\ (^0C)^{-1})\times \Delta (123\ ^0C)]}[/tex]
[tex]{\rho_2}=1.118\times 10^4\ kg/m^3}[/tex]
