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
PHY 004C >CUSTOM<
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)
- The average coefficient of linear expansion of copper is 17 106 (C)1. The Statue of Liberty is 93 in tall on a summer morning when the temperature is 25C. Assume the copper plates covering the statue are mounted edge to edge without expansion joints and do not buckle or bind on the framework supporting them as the day grows hot. What is the order of magnitude of the statues increase in height? (a) 0.1 mm (b) 1 mm (c) 1 cm (d) 10 cm (e) 1 marrow_forwardA 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_forwardTwo concrete spans that form a bridge of length L are placed end to end so that no room is allowed for expansion (Fig. P16.63a). If a temperature increase of T occurs, what is the height y to which the spans rise when they buckle (Fig. P16.63b)?arrow_forward
- Beryllium 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_forwardEqual masses of substance A at 10.0C and substance B at 90.0C are placed in a well-insulated container of negligible mass and allowed to come to equilibrium. If the equilibrium temperature is 75.0Q which substance has the larger specific heat? (a) substance A (b) substance B (c) The specific heats are identical. (d) The answer depends on the exact initial temperatures. (e) More information is required.arrow_forwardThe rectangular plate shown in Figure P16.60 has an area Ai equal to w. If the temperature increases by T, each dimension increases according to Equation 16.4, where is the average coefficient of linear expansion. (a) Show that the increase in area is A = 2Ai T. (b) What approximation does this expression assume?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:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning