Question

A steel tank is completely filled with 2.80 m3 of ethanol when both the tank and the ethanol are at a temperature of 33.0 °С Part A When the tank and its contents have cooled to 18.5 C, what additional volume of ethanol can be put into the tank? Express your answer using two significant figures.

Answer 1

The coefficient of thermal expansion of steel is as follows: a =12x100K-? The coefficient of volume expansion of ethanol is as follows: B = 750x10K-1 From the given data, the change in temperature in kelvin scale is as follows: AT = (33.0 °C +273) K-(18.5°C +273)K = 14.5K The change in volume of the steel tank is as follows: AV tank =V) (3a)(AT) = (2.80 mº)(3(12x10-6 K-'))(14.5 K) = 1.46x10-3 m The change in volume of the ethanol is as follows: AV ethanol =V (B)(AT) = (2.80 m)(750x10-K-)(14.5 K) = 30.45x10-3 m Hence, the amount of ethanol added is as follows: AV = AV ethanol – AV tank = 30.45x10-' m² -1.46x10-m = 28.99x10-2 m ~ 29x10-? m?