College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

Chapter
Section

College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
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=10.0Î¿C to T2=30.0Î¿C . The co-efficient of volume expansion ( Î²ct ) of carbon tetrachloride is 5.81Ã—10âˆ’4/Î¿C . The co-efficient of volume expansion ( Î²s ) of steel is 33Ã—10âˆ’6/Î¿C .

Formula to calculate the volume of carbon tetrachloride spilled is,

Vsp=Î”Vctâˆ’Î”Vs Â Â Â Â Â  (I)

• Î”Vct is the change in volume of carbon tetrachloride.
• Î”Vs is the change in volume of steel.

Formula to calculate change in volume of carbon tetrachloride is,

Î”Vct=Î²ctV0(T2âˆ’T1) Â Â Â Â Â  (II)

Formula to calculate change in volume of steel is,

Î”Vs=Î²sV0(T2âˆ’T1) Â Â Â Â Â  (III)

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

Vsp=(Î²ctâˆ’Î²s)V0(T2âˆ’T1)

Substitute 50

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