Step-by-step solution
We start by substituting the expression for the change in length from the thermal expansion equation into the tensile stress equation, and then
do some algebraic simplification.
The equation we just found does not depend on the initial length. We know all the values needed to calculate the tensile stress in the aluminum
rod.
An aluminum rod with a radius of 0.025 meters (about one inch) exerts more than 60,000 newtons of force (equivalent to the weight of a large
elephant) against perfectly rigid supports when its temperature increases 20 C°! In this problem, we have ignored the expansion of the
concrete in which the aluminum is embedded.
Step Reason
1. F/A = Y(ǻL/Li) tensile stress equation
2. ǻL = LiĮǻT thermal expansion equation
3. Substitute equation 2 into equation 1
4. F/A = YĮǻT Licancels out
Step Reason
5. enter values
6. F/A = 3.2×10^7 N/m^2 multiply
18.10 - Thermal expansion of water
Water exhibits particularly interesting expansion properties when it nears its freezing
point. Above 4°C, water expands with temperature, as most liquids do. However, water
also expands as it cools from 4°C to 0°C, a significant and unusual phenomenon.
Below 0° water once again contracts as it cools. The consequence is that liquid water is
most dense at a temperature of around 4°C.
This pattern of expansion means that lakes and other bodies of water freeze from the
top down. Why? In colder climates, as the autumn or winter seasons approach and the
air temperature drops to near freezing or below, the water in a lake cools. When the
water is cold but still above 4°C, it contracts when it chills. Since it becomes denser, it
sinks. This brings warmer water to the surface, which cools in turn. Eventually, the
entire lake reaches 4°C. But when the top layer then becomes colder still, it no longer
sinks. Below 4°C, the water expands, becoming less dense. It floats atop the warmer
water.
As the cold water at the top of the lake further cools and freezes, it forms a floating layer
of ice that insulates the water below. Water is also atypical in that its solid form, ice, is
less dense than its liquid form and floats on top of it. Fish and other aquatic life can live
in the relatively warm (and liquid) water below, protected by a shield of ice.
If water always expanded with increasing temperature for all temperatures above 0°C,
and contracted with decreasing temperature, the coldest water would sink to the bottom
where it might never warm up. Water’s negative coefficient of expansion in the temperature range from 0°C to 4°C is crucial to life on Earth. If
ice did not float, oceans and lakes would freeze from the bottom to the top. This would increase the likelihood that they would freeze entirely,
since they would not have a top layer of ice to insulate the liquid water below and their frozen depths would not be exposed to warm air during
the spring and summer.
Thermal expansion of water
Water contracts and sinks as it cools,
until 4°C
From 4°C to 0°C, water expands and
stays on top
Then ice forms on top and floats