A steel tank is completely filled with 2.80 m3 of ethanol when both the tank and the ethanol are at a temperature of 32.0°C. When the tank and its contents have c??led to 18.0°C, what additional volume of ethanol can be put into the tank?
Solution 18E Step 1 of 4: Normally solids and liquids with positive expansion coefficient expands or increases its dimensions when they are heated or temperature is increased and converse on cooling. Becauses atoms starts vibrating and increases the dimension following the atomic vibration in crystal is directly proportional to the square of distance between the two atoms as shown below, Change in volume for change in temperature, V = V T0………...1 Where V is change in volume, is coefficient of volume expansion, V 0 initial volume and T is change in temperature. Step 2 of 4: This problem involves the volume compression of the steel and of the ethanol. The volume of ethanol can be added after cooling depends on the difference between the volume changes for these two materials, both given by Eq. (1). 6 That is coefficient of volume expansion for ethanol , =e1120 × 10 /k 6 Similarly coefficient of linear expansion for steel , s= 12 × 10 /k Using = 3 s 3 =s3(12 × 10 /k)6 6 s 36 × 10 /k 6 Therefore, the coefficient of volume expansion for steel is 36 × 10 /k. The ethanol will compress more as its coefficient of volume expansion is greater than that of steel.