Physics: Principles with Applications
6th Edition
ISBN: 9780130606204
Author: Douglas C. Giancoli
Publisher: Prentice Hall
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Question
Chapter 13, Problem 21P
(a)
To determine
To calculate: The change in length of the mercury in the tube on the basis of information provided below.
(a)
Expert Solution
Answer to Problem 21P
The change in the length of the mercury in the tube is 6.1 cm .
Explanation of Solution
Given:
Original volume of the glass with Hg= V0bulb = 0.255cm3
Change in volume = ΔVglass=V0bulbβglassΔT
Change in Hg volume = ΔVHg=V0bulbβHgΔT
Diameter of the Hg tube = 1.40×10−2cm
Change in temperature = ΔT = 33°C−11.5°C
Formula used:
Write the expression for the change in the volume.
(δL)πr02=ΔVHg−ΔVglass(δL)πr02=V0bulbβHgΔT−V0bulbβglassΔT(δL)=V0bulbπr02ΔT(βHg−βglass)
Where δL is the change in the length of the tube .
Calculation:
Substitute the values in the above expression.
δL=V0bulbπr02ΔT(βHg−βglass)=V0bulbπ(d0/2)2ΔT(βHg−βglass)=4V0bulbπd02ΔT(βHg−βglass)=4(0.255cm3)π(1.40×10−2cm)2(33°C−11.5°C)[(180−9)×10−6/C°]=6.1cm
Conclusion:
The expansion of the mercury in the tube is due to the heat. The change in the length of the mercury tube is 6.1 cm .
(b)
To determine
To calculate: The formula for the change in the length of the mercury tube.
(b)
Expert Solution
Answer to Problem 21P
The derived formula for the change in length due to expansion is 4V0bulbπd02ΔT(βHg−βglass) .
Explanation of Solution
Given:
Original volume of the glass with Hg= V0bulb
Change in volume = ΔVglass=V0bulbβglassΔT
Change in Hg volume = ΔVHg=V0bulbβHgΔT
Diameter of the Hg tube
Change in temperature = ΔT
Calculation:
V0BulbΔVglass=V0bulbβglassΔTΔVHg=V0bulbβHgΔT(δL)πr02=ΔVHg−ΔVglass=V0bulbβHgΔT−V0bulbβglassΔT(δL)=V0bulbπr02ΔT(βHg−βglass)=V0bulbπ(d0/2)2ΔT(βHg−βglass)=4V0bulbπd02ΔT(βHg−βglass)
Conclusion:
The derived formula for the change in length due to expansion is 4V0bulbπd02ΔT(βHg−βglass) .
Chapter 13 Solutions
Physics: Principles with Applications
Ch. 13 - Prob. 1QCh. 13 - Prob. 2QCh. 13 - Prob. 3QCh. 13 - Prob. 4QCh. 13 - Prob. 5QCh. 13 - Prob. 6QCh. 13 - Prob. 7QCh. 13 - Prob. 8QCh. 13 - Prob. 9QCh. 13 - Prob. 10Q
Ch. 13 - Prob. 11QCh. 13 - Prob. 12QCh. 13 - Prob. 13QCh. 13 - Prob. 14QCh. 13 - Prob. 15QCh. 13 - Prob. 16QCh. 13 - Prob. 17QCh. 13 - Prob. 18QCh. 13 - Prob. 19QCh. 13 - Prob. 20QCh. 13 - Prob. 21QCh. 13 - Prob. 22QCh. 13 - Prob. 23QCh. 13 - Prob. 27QCh. 13 - How does the number of atoms in a 27.5-gram gold...Ch. 13 - Prob. 2PCh. 13 - (a) “Room temperature” is often taken to be 68°F....Ch. 13 - Prob. 4PCh. 13 - Prob. 5PCh. 13 - Prob. 6PCh. 13 - The Eiffel Tower (Fig. 13-31 [) is built of...Ch. 13 - Prob. 8PCh. 13 - Prob. 9PCh. 13 - To what temperature would you have to heat a brass...Ch. 13 - Prob. 11PCh. 13 - To make a secure fit. rivets that are larger than...Ch. 13 - An ordinary glass is filled to the brim with 450.0...Ch. 13 - An aluminum sphere is 8.75 cm in diameter. What...Ch. 13 - Prob. 15PCh. 13 - Prob. 16PCh. 13 - An aluminum bar has the desired length when at...Ch. 13 - The pendulum in a grandfather clock is made of...Ch. 13 - Prob. 19PCh. 13 - Prob. 20PCh. 13 - Prob. 21PCh. 13 - Prob. 22PCh. 13 - Prob. 23PCh. 13 - Prob. 24PCh. 13 - Prob. 25PCh. 13 - Prob. 26PCh. 13 - Prob. 27PCh. 13 - Prob. 28PCh. 13 - Prob. 29PCh. 13 - Prob. 30PCh. 13 - Prob. 31PCh. 13 - Prob. 32PCh. 13 - Prob. 33PCh. 13 - Prob. 34PCh. 13 - Prob. 35PCh. 13 - Prob. 36PCh. 13 - Prob. 37PCh. 13 - Prob. 38PCh. 13 - Prob. 39PCh. 13 - Prob. 40PCh. 13 - Prob. 41PCh. 13 - Prob. 42PCh. 13 - Prob. 43PCh. 13 - Prob. 44PCh. 13 - Prob. 45PCh. 13 - Prob. 46PCh. 13 - Prob. 47PCh. 13 - Prob. 48PCh. 13 - Prob. 49PCh. 13 - Prob. 50PCh. 13 - Prob. 51PCh. 13 - Prob. 52PCh. 13 - Prob. 53PCh. 13 - Prob. 54PCh. 13 - Prob. 55PCh. 13 - Prob. 56PCh. 13 - Prob. 57PCh. 13 - Prob. 58PCh. 13 - Prob. 59PCh. 13 - Prob. 60PCh. 13 - Prob. 61PCh. 13 - Prob. 62PCh. 13 - Prob. 63PCh. 13 - Prob. 64PCh. 13 - Prob. 65PCh. 13 - Prob. 66PCh. 13 - Prob. 67PCh. 13 - Prob. 68PCh. 13 - Prob. 69PCh. 13 - Prob. 70PCh. 13 - Prob. 71PCh. 13 - Prob. 72PCh. 13 - Prob. 73GPCh. 13 - Prob. 74GPCh. 13 - Prob. 75GPCh. 13 - Prob. 76GPCh. 13 - Prob. 77GPCh. 13 - Prob. 78GPCh. 13 - Prob. 79GPCh. 13 - Prob. 80GPCh. 13 - Prob. 81GPCh. 13 - Prob. 82GPCh. 13 - Prob. 83GPCh. 13 - Prob. 84GPCh. 13 - Prob. 85GPCh. 13 - Prob. 86GPCh. 13 - Prob. 87GPCh. 13 - Prob. 88GPCh. 13 - Prob. 89GPCh. 13 - Prob. 90GPCh. 13 - Prob. 91GP
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