<< Chapter < Page Chapter >> Page >

In general, objects will expand with increasing temperature. Water is the most important exception to this rule. Water expands with increasing temperature (its density decreases ) when it is at temperatures greater than 4 º C ( 40 º F ) size 12{4°"C " \( "40"°F \) } {} . However, it expands with decreasing temperature when it is between + 4 º C size 12{+4°C} {} and 0 º C size 12{0°C} {} ( 40 º F size 12{ \( "40"°F} {} to 32 º F ) size 12{"32"°F \) } {} . Water is densest at + 4 º C size 12{+4°C} {} . (See [link] .) Perhaps the most striking effect of this phenomenon is the freezing of water in a pond. When water near the surface cools down to 4 º C size 12{4°C} {} it is denser than the remaining water and thus will sink to the bottom. This “turnover” results in a layer of warmer water near the surface, which is then cooled. Eventually the pond has a uniform temperature of 4 º C size 12{4°C} {} . If the temperature in the surface layer drops below 4 º C size 12{4°C} {} , the water is less dense than the water below, and thus stays near the top. As a result, the pond surface can completely freeze over. The ice on top of liquid water provides an insulating layer from winter’s harsh exterior air temperatures. Fish and other aquatic life can survive in 4 º C size 12{4°C} {} water beneath ice, due to this unusual characteristic of water. It also produces circulation of water in the pond that is necessary for a healthy ecosystem of the body of water.

A graph of density of freshwater in grams per cubic centimeter versus temperature in degrees Celsius. The line is convex up. At zero degrees C, the density is just under zero point nine nine nine five grams per cubic centimeter. The density then increases at a decreasing rate until it hits a peak of about zero point nine nine nine nine seven grams per cubic centimeter at about four degrees C. Above four degrees C, the density decreases with increasing temperature.
The density of water as a function of temperature. Note that the thermal expansion is actually very small. The maximum density at + 4 º C size 12{+4°C} {} is only 0.0075% greater than the density at 2 º C size 12{2°C} {} , and 0.012% greater than that at 0 º C size 12{0°C} {} .

Making connections: real-world connections—filling the tank

Differences in the thermal expansion of materials can lead to interesting effects at the gas station. One example is the dripping of gasoline from a freshly filled tank on a hot day. Gasoline starts out at the temperature of the ground under the gas station, which is cooler than the air temperature above. The gasoline cools the steel tank when it is filled. Both gasoline and steel tank expand as they warm to air temperature, but gasoline expands much more than steel, and so it may overflow.

This difference in expansion can also cause problems when interpreting the gasoline gauge. The actual amount (mass) of gasoline left in the tank when the gauge hits “empty” is a lot less in the summer than in the winter. The gasoline has the same volume as it does in the winter when the “add fuel” light goes on, but because the gasoline has expanded, there is less mass. If you are used to getting another 40 miles on “empty” in the winter, beware—you will probably run out much more quickly in the summer.

Fuel gauge pointing to empty.
Because the gas expands more than the gas tank with increasing temperature, you can’t drive as many miles on “empty” in the summer as you can in the winter. (credit: Hector Alejandro, Flickr)

Calculating thermal expansion: gas vs. gas tank

Suppose your 60.0-L (15.9-gal) steel gasoline tank is full of gas, so both the tank and the gasoline have a temperature of 15 . 0 º C size 12{"15" "." 0°C} {} . How much gasoline has spilled by the time they warm to 35 . 0 º C size 12{"35" "." 0°C} {} ?

Strategy

The tank and gasoline increase in volume, but the gasoline increases more, so the amount spilled is the difference in their volume changes. (The gasoline tank can be treated as solid steel.) We can use the equation for volume expansion to calculate the change in volume of the gasoline and of the tank.

Solution

1. Use the equation for volume expansion to calculate the increase in volume of the steel tank:

Δ V s = β s V s Δ T . size 12{ΔV rSub { size 8{s} } =β rSub { size 8{s} } V rSub { size 8{s} } ΔT} {}

2. The increase in volume of the gasoline is given by this equation:

Δ V gas = β gas V gas Δ T . size 12{ΔV rSub { size 8{"gas"} } =β rSub { size 8{"gas"} } V rSub { size 8{"gas"} } ΔT} {}

3. Find the difference in volume to determine the amount spilled as

V spill = Δ V gas Δ V s . size 12{V rSub { size 8{"spill"} } =ΔV rSub { size 8{"gas"} } - ΔV rSub { size 8{s} } } {}

Alternatively, we can combine these three equations into a single equation. (Note that the original volumes are equal.)

V spill = β gas β s V Δ T = 950 35 × 10 6 / º C 60 . 0 L 20 . 0 º C = 1 . 10 L .

Discussion

This amount is significant, particularly for a 60.0-L tank. The effect is so striking because the gasoline and steel expand quickly. The rate of change in thermal properties is discussed in Heat and Heat Transfer Methods .

If you try to cap the tank tightly to prevent overflow, you will find that it leaks anyway, either around the cap or by bursting the tank. Tightly constricting the expanding gas is equivalent to compressing it, and both liquids and solids resist being compressed with extremely large forces. To avoid rupturing rigid containers, these containers have air gaps, which allow them to expand and contract without stressing them.

Practice Key Terms 4

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, College physics ii. OpenStax CNX. Nov 29, 2012 Download for free at http://legacy.cnx.org/content/col11458/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics ii' conversation and receive update notifications?

Ask