Answer:
[tex]T_2=24.98^oC[/tex]
The final equilibrium temperature of the copper-oil system is 24.98 degree Celsius
Explanation:
Assumptions:
No heat Transfer to surroundings=Q=0
No work done=W=0
Specific heat capacity of copper at constant volume=[tex]C_v=0.386\ KJ/Kg.K[/tex]
Specific heat capacity of light oil at constant volume=[tex]C_v[/tex]=[tex]1.8\ KJ/kg.K[/tex]
Density of copper=[tex]\rho_c=8900Kg/m^3[/tex]
Density of light oil=[tex]\rho_o=910\ Kg/m^3[/tex]
1 L=0.001 m^3, 200 L=0.2 m^3
Mass of copper=[tex]m_c=\rho*v[/tex]=[tex]8900*0.001=8.9\ Kg[/tex]
Mass of light oil=[tex]m_o=\rho_o*v_o=910*0.2=182\ Kg[/tex]
According to first Law:
Q-W=ΔU
According to assumptions:
ΔU=0
[tex]m_cC_v_(T_2-T_1_c)+m_oC_v(T_2-T_1_o)[/tex]=0
[tex]8.9*0.386(T_2-500)+182*1.8(T_2-20)=0\\T_2=24.98^oC[/tex]
The final equilibrium temperature of the copper-oil system is 24.98 degree Celsius
