When a ball of copper is heated, its diameter is observed to increase by 0.01%. We can say that it's volume increases by approximately

Question

BlackTom AI · Accepted Answer

The problem says a copper ball’s diameter increases by 0.01% when heated, and asks for the approximate relative change in volume due to this diameter change.
Option 1: 0.01% — This would be the relative change in diameter, not in volume. Since volume scales with the cube of the linear dimension, the volume change is larger than the diameter change.
Option 2: 0.03% — This comes from the fact that for small changes, ΔV/V ≈ 3 (ΔD/D) for a sphere, because V ∝ D^3. Here ΔD/D = 0.01% = 0.0001, so ΔV/V ≈ 3 × 0.0001 = 0.0003 = 0.03%. This aligns with the cubic dependence of volume on diameter.
Option 3: 0.000001% — This is far too small by several orders of magnitude. It would correspond to a much smaller exponent or an error in applying the proportionality, which is not the case for a simple geometric scaling.
Option 4: 0.02% — This is close but does not match the cubic relationship. It would arise if volume depended on D^2 (which it does not for a sphere), or if a miscalculation of the factor 3 occurred.
In summary, since volume scales with the cube of diameter, a 0.01% increase in diameter yields approximately a 0.03% increase in volume, via the relation ΔV/V ≈ 3 ΔD/D for small changes.

PHYS_V 157 201 2024W2 Reading Quiz Week 2

When a ball of copper is heated, its diameter is observed to increase by 0.01%. We can say that it's volume increases by approximately

查看解析

登录即可查看完整答案

类似问题

What is the difference between coefficient of linear expansion (α) and coefficient of volume expansion (β)?

Which of the following is the correct set of formula for thermal expansion in solid objects?

What happens to the cavity inside an object if the temperature is increased?

What is thermal expansion?

An aluminum plate has a circular hole. If the temperature of the plate increases, what happens to the size of the hole?

双金属板由两种不同热膨胀系数的材料组成。板材顶部的热膨胀系数小于底部。如果整个盘子的温度升高，盘子会怎样？

Some iron has a coefficient of linear expansion of 12 x 10-6 K-1. A 100mm length of iron piping is heated through 20 K. The pipe extends by:

A bimetal plate consists of two materials of different coefficients of thermal expansion. The coefficient of thermal expansion of the top part of the plate is less than the bottom part. If the temperature of the entire plate increases, what happens to the plate?

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单