   Chapter 10, Problem 25P

Chapter
Section
Textbook Problem

The average coefficient of volume expansion for carbon tetrachloride is 5.81 × 10−4 (°C)−1. If a 50.0-gal steel container is filled completely with carbon tetrachloride when the temperature is 10.0°C, how much will spill over when the temperature rises to 30.0°C?

To determine
The volume of carbon tetrachloride spilled.

Explanation

Given Info: The volume of steel container ( V0 ) is 50.0 gal. The temperature changes from T1=10.0οC to T2=30.0οC . The co-efficient of volume expansion ( βct ) of carbon tetrachloride is 5.81×104/οC . The co-efficient of volume expansion ( βs ) of steel is 33×106/οC .

Formula to calculate the volume of carbon tetrachloride spilled is,

Vsp=ΔVctΔVs       (I)

• ΔVct is the change in volume of carbon tetrachloride.
• ΔVs is the change in volume of steel.

Formula to calculate change in volume of carbon tetrachloride is,

ΔVct=βctV0(T2T1)       (II)

Formula to calculate change in volume of steel is,

ΔVs=βsV0(T2T1)       (III)

From Equations (I) , (II) and (III),

Vsp=(βctβs)V0(T2T1)

Substitute 50

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