Gas law
Observe the relationship between pressure and temperature in a sealed volume using the smartphone barometer.
The ideal gas law, PV = nRT, is one of the most fundamental equations in physics. At constant volume (sealed jar), it predicts that pressure is proportional to absolute temperature. By placing a smartphone barometer in an airtight jar and changing the temperature, you can verify this law and even estimate absolute zero by extrapolating the P(T) graph to P = 0.
Activity overview:
The student places their smartphone in an airtight jar and records pressure with the FizziQ barometer. By exposing the jar to different temperatures, they verify Gay-Lussac's law.
Level:
High School
FizziQ
Author:
Duration (minutes) :
30
What students will do :
- Measure atmospheric pressure variations with the smartphone barometer
- Verify Gay-Lussac's law (P proportional to T at constant V)
- Plot a P(T) graph and perform a linear extrapolation
- Estimate absolute zero from the P(T) extrapolation
- Understand the limitations of the ideal gas model
Scientific concepts:
- Ideal gas law (PV = nRT)
- Gay-Lussac's law
- Atmospheric pressure
- Absolute temperature (kelvin)
- Absolute zero
- Relative humidity
- Dew point
Sensors:
- Barometer
- Thermometer (if available)
- Hygrometer (if available)
Material needed:
- Smartphone or tablet with FizziQ
- An airtight glass jar (mason jar type)
- Ice or a freezer
- Warm water (40-50°C)
- External thermometer (if the phone lacks one)
Experimental procedure:
Verify that your smartphone has a barometer. A temperature sensor and hygrometer are a bonus but not required.
Open FizziQ and configure simultaneous recording of the Barometer and any other available sensors (thermometer, hygrometer).
Start the recording and place the smartphone in the airtight jar. Seal carefully.
Leave the system at room temperature for 2 minutes to stabilize. Note P₀ and T₀.
Place the jar in a freezer or surround it with ice. Wait 5 to 10 minutes for the temperature to drop by at least 15°C.
Observe the evolution: pressure decreases with temperature, relative humidity increases.
Remove the jar from the cold and warm it gently (warm water around the jar, 40-50°C). The pressure rises.
Stop the recording and analyze the data.
For each data point, calculate the ratio P/T (in kelvin). Verify that this ratio remains constant to within a few percent.
Plot P versus T (in kelvin). A straight line through the origin confirms Gay-Lussac's law. Extrapolation to P = 0 gives an estimate of absolute zero.
Expected results:
The pressure decreases by 5 to 10 hPa during a 20°C cooling. The ratio P/T (in kelvin) remains constant to 1-2%. Relative humidity increases in the cold, with possible condensation. The graph P(T in kelvin) is a straight line. Extrapolation to P = 0 gives approximately -273°C.
Scientific questions:
- Why must the ratio P/T be calculated in kelvin rather than Celsius?
- What factors explain why P/T is not perfectly constant?
- How could you improve the precision of the absolute zero estimate?
- Why does the phone's internal heat generation affect the results?
- What would happen if the jar seal leaked during the experiment?
- How does this experiment relate to the behavior of real gases?
Scientific explanations:
Gay-Lussac's law states that at constant volume, gas pressure is proportional to absolute temperature: P = (nR/V) × T. The ratio P/T is constant.
For a cooling of 20°C to 0°C (from 293 K to 273 K), the pressure drops by 6.8%, representing about 7 hPa. This is clearly detectable by the smartphone barometer.
The smartphone barometer has a resolution of 0.01 hPa, which is more than sufficient to detect this variation of several hPa.
Relative humidity increases when cooled because cold air holds less water vapor at saturation. If the air reaches 100% humidity, condensation (fog) can form inside the jar.
Extrapolation of the P(T) line toward P = 0 should give T ≈ -273°C, absolute zero. This is an elegant experimental demonstration of the kelvin scale.
Deviations from the ideal model come mainly from two factors: the smartphone itself generates heat (raising the internal temperature above the environment), and the jar seal may not be perfectly airtight.
The complete ideal gas law is PV = nRT, with R = 8.314 J/(mol·K). At constant volume and amount of gas, P and T are directly proportional.
Extension activities:
- Why must the ratio P/T be calculated in kelvin rather than Celsius?
- What factors explain why P/T is not perfectly constant?
- How could you improve the precision of the absolute zero estimate?
- Why does the phone's internal heat generation affect the results?
- What would happen if the jar seal leaked during the experiment?
- How does this experiment relate to the behavior of real gases?
Frequently asked questions:
Q: My smartphone does not have an ambient thermometer.
R: Most models do not (only some Samsung Galaxy phones have one). Use an external thermometer or estimate temperature from the barometric data.
Q: The pressure changes even without temperature change.
R: Weather changes cause the atmospheric baseline to shift. Keep the experiment short (< 30 minutes) to minimize this effect.
Q: How do I convert °C to kelvin?
R: T(K) = T(°C) + 273.15. For example: 20°C = 293.15 K.
Q: Can I heat the jar more for a larger temperature range?
R: Avoid heating above 50°C as this may damage the smartphone. A range of 0°C to 40°C is sufficient for a clear demonstration.