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# What is the Coldest Possible Temperature? Estimating Absolute Zero. (page 2)

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Author: Jerry Silver

### Expected Results

The accepted value for absolute zero is 0 K or –273°C or –459.7°F. However, because the first part of this experiment is a ballpark measurement, values anywhere from –175 to –350°C are reasonable extrapolations. Although this is a wide range, the concept that extrapolating the volume versus temperature curve until the volume goes to zero is significant. Statistically, we know we are on very shaky ground because we are generating data points that are far removed from the temperature we are extrapolating to.

### Why It Works

Charles's law states that T1/V1 = T2/V2. This can be interpreted as saying that the volume of a gas is directly proportional to the temperature. The lowest temperature conceivable is the temperature when the gas contracts to a zero volume. This can never actually occur. If we extrapolate the linear relationship between temperature and volume to zero volume, you can determine a value for absolute zero.

Similarly, Gay-Lussac's law states that T1/P1 = T2/P2. Absolute zero is the temperature where the temperature pressure line is extrapolated to zero pressure.

### Other Things to Try

The accuracy of this measurement can be improved on by using the Gay-Lussac's apparatus and extrapolating the temperature versus pressure curve to zero pressure, as shown in Figure 91-3.

Two different sets of measurements of temperature versus pressure are shown in Figure 91-4.

The point where the pressure extrapolates to zero is interpreted as absolute zero, as shown in Figure 91-5.

One source of error in determining the change in volume with temperature is the presense of water vapor in the flask. Use of oil instead of water to immerse the flask in avoids this problem. This is a messier but more accurate way to estimate absolute zero.

Absolute zero can be determined by measuring the speed of sound at different temperatures, as described in "Determining Absolute Zero Using a Tuning Fork," by Jeffrey D. Goldader (The Physics Teacher 46, April 2008, 206–209).

### The Point

Absolute zero cannot be measured directly. It can be determined by extrapolating measurements of pressure versus temperature to zero pressure. Similarly, absolute zero can be determined by extrapolating measurements of volume versus temperature to zero volume.

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