Concept explainers
The initial length L, change in temperature ΔT, and change in length ΔL of four rods are given in the following table. Rank the rods according to their coefficients of thermal expansion, greatest first.
Rod | L(m) | ΔT(C°) | ΔL (m) |
a | 2 | 10 | 4 × 10−4 |
b | 1 | 20 | 4 × 10−4 |
c | 2 | 10 | 8 × 10−4 |
d | 4 | 5 | 4 × 10−4 |
To rank
the four rods according to their coefficients of thermal expansion.
Answer to Problem 1Q
Solution:
The ranking of the rods according to their coefficients of thermal expansion is
Explanation of Solution
1) Concept:
Using the Equation 18-9 for the change in the length of rod
2) Formula:
Where
3) Given:
i) The length of rod a is
ii) The length of rod b is
iii) The length of rod c is
iv) The length of rod d is
v) The change in temperature of rod a is
vi) The change in temperature of rod b is
vii) The change in temperature of rod c is
viii) The change in temperature of rod d is
ix) The change in the length of rod a is
x) The change in the length of rod b is
xi) The change in the length of rod c is
xii) The change in the length of rod d is
4) Calculations:
Using Equation 18-9- If the temperature of the metal rod of length L is released by an amount
Where
Therefore, the coefficient
Let
So, for rod a;
Similarly, for rod b;
For rod c;
And for rod d;
Therefore, we get
Conclusion:
Using the formula for change in length due to linear expansion, we can rank the rods according to their coefficient of thermal expansion.
Want to see more full solutions like this?
Chapter 18 Solutions
Fundamentals of Physics, Extended
Additional Science Textbook Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
Essential University Physics: Volume 2 (3rd Edition)
Essential University Physics (3rd Edition)
Mathematical Methods in the Physical Sciences
Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)
College Physics (10th Edition)
- A sample of a solid substance has a mass m and a density 0 at a temperature T0. (a) Find the density of the substance if its temperature is increased by an amount T in terms of the coefficient of volume expansion b. (b) What is the mass of the sample if the temperature is raised by an amount T?arrow_forwardBeryllium has roughly one-half the specific heat of water (H2O). Rank the quantities of energy input required to produce the following changes from the largest to the smallest. In your ranking, note any cases of equality, (a) raising the temperature of 1 kg of H2O from 20C to 26C (b) raising the temperature of 2 kg of H2O from 20C to 23C (c) raising the temperature of 2 kg of H2O from 1C to 4C (d) raising the temperature of 2 kg of beryllium from 1C to 2C (e) raising the temperature of 2 kg of H2O from -1C to 2Carrow_forwardAt 25.0 m below the surface of the sea, where the temperature is 5.00C, a diver exhales an air bubble having a volume of 1.00 cm3. If the surface temperature of the sea is 20.0C, what is the volume of the bubble just before it breaks the surface?arrow_forward
- What is the change in length of a 3.4-cm-long column of mercury if its temperature changes from 35 ºC to 35.3 ºC, assuming the mercury is unconstrained? The thermal coefficient of expansion of mercury is 6×10-5 /oC.arrow_forwardAn aluminum can is filled to the brim with a liquid. The can and the liquid are heated so their temperatures change by the same amount. The can's initial volume at 8 °C is 9.3 × 10-4 m³. The coefficient of volume expansion for aluminum is 69 × 10-6 (Cº)-¹. When the can and the liquid are heated to 86 °C, 8.5 x 10-6 m³ of liquid spills over. What is the coefficient of volume expansion of the liquid? B₁ =arrow_forwardCoefficient of linear expansion of a certain metal is 3.0 x10-6 °C¯1. what is the coefficient of volume expansion of this metal? O 6.0 ×10-6 °c-1 O 9.0 x10-6 °c-1 О 3.0 х10-6 оС-1 О 1.5 х10-6 ос-1arrow_forward
- A circular hole in a copper plate has a diameter 4.045 cm at 20.000 °C. What is its diameter when the temperature of the plate is raised by 243 C°? The coefficient of volume expansion of copper is 51 x 10-6 C°. Select one: O 4.062 cm O 4.095 cm O Answer Not Given O 4.379 cm O 4.546 cmarrow_forwardThe area A of a rectangular plate is ab = 1.4 m?. Its coefficient of linear expansion is a = 22 x 10° /C°. After a temperature rise AT = 17°C, side a is longer by Aa and side b is longer by Ab (see the figure). Neglecting the small quantity (AaAb)/ab, find AA. %3D a Да Aa · Ab Abarrow_forwardA glass is filled to the brim with 330.0 mL of water at 100.0 ∘C . If the temperature of glass and water is decreased to 20.0 ∘C, how much water could be added to the glass? Answer in terms of ΔV.arrow_forward
- The second pic is the rquired number of tolerance needed in the answerarrow_forwardA lead rod is heated from 30°C to 50°C. After the temperature is raised, the rod lengthens 0.00013m. what is the initial length of the lead rod? The coefficient of linear expansion for lead is 29x10^-6/°C.arrow_forwardA copper rod is 2.93 m in length at 20.0 °C. What is the length of the rod if the temperature is raised to 120.0 °C? The coefficient of linear expansion of copper is 17 × 10–6/C°. Express your answer in mm (millimeter)arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- College PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningAn Introduction to Physical SciencePhysicsISBN:9781305079137Author:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar TorresPublisher:Cengage Learning