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.
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