Answer:0.548 gallon
Explanation:
Given
Average coefficient of volume expansion for carbon Tetrachloride [tex]\beta =5.81\times 10^{-4} /^{\circ}C[/tex]
Volume of steel container [tex]V=50 gallon[/tex]
Initial temperature [tex]T_i=10^{\circ}C[/tex]
Final temperature [tex]T_f=30^{\circ}C[/tex]
[tex]\Delta T=20^{\circ}C[/tex]
Coefficient of expansion for steel is [tex]\alpha =11\times 10^{-6}[/tex]
[tex]\beta =3\alpha =3\times 11\times 10^{-6}[/tex]
[tex]\beta =33\times 10^{-6}/^{\circ}C[/tex]
[tex]\Delta V_{spill}=\Delta V_{liquid}-\Delta V_{steel}[/tex]
[tex]\Delta V_{spill}=(\beta _{carbon}-\beta _{steel})V_0(\Delta T)[/tex]
[tex]\Delta V_{spill}=(5.81\times 10^{-4}-33\times 10^{-6})50\times 20[/tex]
[tex]\Delta V_{spill}=0.548\ gallon[/tex]
