contestada

A certain steel alloy has a coefficient of linear expansion of 1.10 × 10-5 °C) 1 A 60.0-gallon container, made of this alloy, is filled to the top with turpentine, which has an average coefficent of volume expansion of 9.00 10-4 oC) 1 Initially the temperature is 10.0°C How much turpentine (in gallons) will spill over if the temperature rises to 30.0°C? (Round your answer to at least three decimal places.) gal

Respuesta :

Answer:

[tex]V_F=0.684\ gallon[/tex]

Explanation:

Given:

  • Initial temperature, [tex]T_i=10^{\circ}C[/tex]
  • Final temperature, [tex]T_f=30^{\circ}C[/tex]
  • coefficient of linear expansion of steel alloy, [tex]\alpha_s=1.1\times 10^{-5}\ ^{\circ}C^{-1}[/tex]
  • coefficient of volumetric expansion of turpentine oil, [tex]\beta=9\times 10^{-4}\ ^{\circ}C^{-1}[/tex]
  • final temperature, [tex]T_f=30^{\circ}C[/tex]
  • initial volume of turpentine, [tex]V=60\ gallon[/tex]

We know:

[tex]\beta_s=3\times \alpha_s[/tex]

[tex]\therefore \beta_s=3.3\times 10^{-5}\ ^{\circ}C^{-1}[/tex]

Now the change in volume of vessel:

[tex]\Delta V_s=V.\beta_s.\Delta T[/tex]

[tex]\Delta V_s=60\times 3.3\times 10^{-5}\times 20[/tex]

[tex]\Delta V_s=0.396\ gallon[/tex]

Now the change in volume of oil:

[tex]\Delta V=V.\beta.\Delta T[/tex]

[tex]\Delta V=60\times 9\times 10^{-4}\times 20[/tex]

[tex]\Delta V=1.08\ gallon[/tex]

Therefore the volume that will overflow is:

[tex]V_F=\Delta V-\Delta V_s[/tex]

[tex]V_F=1.08-0.396[/tex]

[tex]V_F=0.684\ gallon[/tex]