   Chapter 10, Problem 19P

Chapter
Section
Textbook Problem

An underground gasoline tank can hold 1.00 × 103 gallons of gasoline at 52.0°F. If the tank is being filled on a day when the outdoor temperature (and the gasoline in a tanker truck) is 95.0°F, how many gallons from the truck can be poured into the tank? Assume the temperature of the gasoline quickly cools from 95.0°F to 52.0°F upon entering the tank.

To determine
The volume of gasoline poured into the tank.

Explanation

Given Info: Volume of gasoline ( V0 ) held by the tank at temperature T0=52.0οF is 1.00×103gallon . The temperature is changed to T=95.0οF . The co-efficient of volume expansion of gasoline ( β ) is 9.6×104/οC .

Formula to calculate the volume of gasoline poured into the tank is,

V=V0[1+β(TT0)]

• β is the co-efficient of volume expansion.

Substitute 25.0 m for L0 , 1.19 cm for ΔL , 2.00οC for T1 and 30.0οC for T2 in the above equation to get α .

V=(1.00×103gallon)[1+(9

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