The Boyle–Charles law experiment investigates the relationship among pressure, volume, and temperature for a fixed amount of gas.
When temperature is kept constant, the volume of a gas is inversely proportional to its pressure. This is Boyle’s law. When pressure is kept constant, the volume of a gas is proportional to its absolute temperature. This is Charles’s law.
Combining these relationships gives the Boyle–Charles law: for a fixed amount of gas, the value obtained by dividing the product of pressure and volume by absolute temperature remains constant.
This article assumes an experiment that measures the relationship between pressure and volume using air trapped in a syringe or cylinder, as well as an experiment that measures the relationship between temperature and volume at constant pressure. It is organized in the order of introduction, precautions, items to record, sample experimental data, calculations, sources of error, an example results section, and discussion examples.
Note:
This article is a study reference for discussing results obtained in physics or chemistry experiments at schools, colleges, and universities. The experimental conditions and measured values shown here are illustrative examples and are not actual experimental results.
Heating or excessively compressing a sealed container may damage the container or its connections. Do not exceed the pressure or heat resistance limits of the equipment. When using hot water or a heated bath, take care to avoid burns, and be alert for damage to glassware and pressure sensors or disconnection and damage of tubing. Follow the laboratory manual and the instructions of your instructor or teaching assistant for actual procedures.
- Boyle’s Law
- Charles’s Law
- Boyle–Charles Law
- Absolute Pressure and Gauge Pressure
- Main Items to Record in the Results
- Sample Experimental Conditions
- Sample Experimental Data
- Calculation Methods
- Main Sources of Error
- Why Pressure and Volume Are Inversely Proportional in Boyle’s Law
- Why Volume and Absolute Temperature Are Proportional in Charles’s Law
- Why Absolute Temperature Is Used Instead of Celsius Temperature
- Why a Graph of Pressure Versus 1/V Is Linear
- Why a Graph of Volume Versus Absolute Temperature Is Linear
- Example of How to Write the Results
- Points to Connect the Results to the Discussion
- Discussion Example
- Summary
Boyle’s Law
For a fixed amount of gas maintained at constant temperature, the product of pressure P and volume V is constant.
PV = constant
Comparing state 1 and state 2 gives the following equation.
P1V1 = P2V2
Therefore, when temperature is constant, volume decreases as pressure increases.
Charles’s Law
For a fixed amount of gas maintained at constant pressure, volume V is proportional to absolute temperature T.
V/T = constant
Comparing state 1 and state 2 gives the following equation.
V1/T1 = V2/T2
Absolute temperature, rather than Celsius temperature, must be used.
T (K) = t (°C) + 273.15
Boyle–Charles Law
For a fixed amount of gas, the relationship among pressure, volume, and absolute temperature is expressed as follows.
PV/T = constant
Comparing state 1 and state 2 gives:
P1V1/T1 = P2V2/T2
This relationship holds well when the amount of gas is constant and the gas behaves approximately as an ideal gas.
Absolute Pressure and Gauge Pressure
The pressure used in gas-law equations is absolute pressure, for which a vacuum is defined as zero pressure.
Absolute pressure = atmospheric pressure + gauge pressure
For example, if atmospheric pressure is 101.3 kPa and the pressure gauge reads 50.0 kPa, the absolute pressure is 151.3 kPa.
A negative gauge pressure means that the pressure is lower than atmospheric pressure.
Main Items to Record in the Results
- Gas used
- Type of container or syringe used to confine the gas
- Atmospheric pressure
- Gauge pressure
- Absolute pressure
- Gas volume
- Celsius temperature
- Absolute temperature
- Product of pressure and volume, PV
- Ratio of volume to absolute temperature, V/T
- Value of PV/T
- Graph of pressure versus 1/V
- Graph of volume versus absolute temperature
- Instrument resolution
- Time required to reach equilibrium under each condition
- Average of repeated measurements
- Room temperature
Sample Experimental Conditions
| Item | Sample Condition |
|---|---|
| Gas used | Air |
| Atmospheric pressure | 101.3 kPa |
| Temperature for Boyle’s law measurement | 25.0 °C |
| Pressure for Charles’s law measurement | 101.3 kPa |
| Initial volume | 50.0 mL |
| Pressure measurement range | Approx. 80–200 kPa |
| Temperature measurement range | Approx. 10–80 °C |
| Pressure sensor resolution | 0.1 kPa |
| Volume scale resolution | 0.5 mL |
Sample Experimental Data
Sample Data for Boyle’s Law
The following illustrative data represent compression of a fixed amount of air at a constant temperature of 25.0 °C.
| Absolute Pressure P (kPa) | Volume V (mL) | PV (kPa·mL) | 1/V (mL−1) |
|---|---|---|---|
| 80.0 | 63.2 | 5056 | 0.0158 |
| 100.0 | 50.4 | 5040 | 0.0198 |
| 120.0 | 42.1 | 5052 | 0.0238 |
| 150.0 | 33.6 | 5040 | 0.0298 |
| 180.0 | 28.1 | 5058 | 0.0356 |
| 200.0 | 25.2 | 5040 | 0.0397 |
Sample Data for Charles’s Law
The following illustrative data represent heating a fixed amount of air at a pressure of 101.3 kPa.
| Temperature t (°C) | Absolute Temperature T (K) | Volume V (mL) | V/T (mL/K) |
|---|---|---|---|
| 10.0 | 283.15 | 47.5 | 0.1678 |
| 20.0 | 293.15 | 49.2 | 0.1678 |
| 30.0 | 303.15 | 50.9 | 0.1679 |
| 40.0 | 313.15 | 52.5 | 0.1677 |
| 60.0 | 333.15 | 55.9 | 0.1678 |
| 80.0 | 353.15 | 59.3 | 0.1679 |
Sample Data for the Boyle–Charles Law
| State | Absolute Pressure P (kPa) | Volume V (mL) | Temperature T (K) | PV/T (kPa·mL/K) |
|---|---|---|---|---|
| 1 | 101.3 | 50.0 | 293.15 | 17.28 |
| 2 | 120.0 | 45.1 | 313.15 | 17.28 |
| 3 | 150.0 | 38.4 | 333.15 | 17.29 |
| 4 | 180.0 | 33.9 | 353.15 | 17.28 |
Calculation Methods
Converting Gauge Pressure to Absolute Pressure
For an atmospheric pressure of 101.3 kPa and a gauge pressure of 48.7 kPa:
P = 101.3 + 48.7
= 150.0 kPa
Converting Celsius Temperature to Absolute Temperature
For a temperature of 40.0 °C:
T = 40.0 + 273.15
= 313.15 K
Calculating Volume Using Boyle’s Law
When a gas initially at 100.0 kPa and 50.4 mL is compressed at constant temperature to 150.0 kPa:
P1V1 = P2V2
V2 = P1V1/P2
= 100.0 × 50.4/150.0
= 33.6 mL
Calculating Volume Using Charles’s Law
When a gas at 20.0 °C and 49.2 mL is heated at constant pressure to 60.0 °C:
V1/T1 = V2/T2
V2 = V1T2/T1
= 49.2 × 333.15/293.15
= 55.9 mL
Calculation Using the Boyle–Charles Law
Suppose state 1 is 101.3 kPa, 50.0 mL, and 293.15 K, while state 2 is 150.0 kPa and 333.15 K. The volume is calculated as follows.
P1V1/T1 = P2V2/T2
V2 = P1V1T2/(P2T1)
= 101.3 × 50.0 × 333.15/(150.0 × 293.15)
= 38.4 mL
Calculating PV/T
For a pressure of 150.0 kPa, volume of 38.4 mL, and temperature of 333.15 K:
PV/T = 150.0 × 38.4/333.15
= 17.29 kPa·mL/K
Mean PV and Relative Deviation
If the mean PV obtained from Boyle’s law measurements is 5048 kPa·mL and one measured value is 5058 kPa·mL:
Relative deviation (%) = |measured value − mean value|/mean value × 100
= |5058 − 5048|/5048 × 100
= 0.20%
Main Sources of Error
| Source of Error | Effect on Measurement | Likely Trend in Results | Improvement |
|---|---|---|---|
| Temperature change during compression or expansion | Violates the constant-temperature condition of Boyle’s law | Rapid compression tends to produce an excessively high pressure reading | Operate slowly and read after temperature has returned to equilibrium |
| Gas leakage | Changes the amount of gas | PV or PV/T does not remain constant | Check seals at connections and the piston |
| Piston friction | Internal and external pressures do not immediately become equal | Values differ between compression and expansion | Use low-friction equipment and approach readings from the same direction |
| Pressure-gauge zero offset | Adds a constant bias to all pressure values | Shifts the graph slope or intercept | Calibrate the zero point before measurement |
| Using gauge pressure as absolute pressure | Substitutes an incorrect pressure into the gas law | Causes especially large error at low pressure | Add atmospheric pressure to convert to absolute pressure |
| Using Celsius temperature directly | Breaks the proportional relationship in Charles’s law | V/T does not remain constant | Always convert to kelvin |
| Temperature difference between gas and constant-temperature bath | Measured temperature differs from the actual gas temperature | Large discrepancy immediately after heating or cooling | Wait until thermal equilibrium is reached |
| Dead volume in syringe and tubing | Gas volume exists outside the indicated scale | Relative error becomes large especially at small volumes | Shorten connecting tubes and correct for dead volume |
| Volume-scale reading error | Shifts calculated PV and V/T | Relative error becomes larger at small volumes | Read the scale with the eye level with the mark |
| Water droplets or water vapor | Changes gas amount or partial pressure | Results tend to deviate from theory at high temperature | Dry the apparatus and correct for water-vapor pressure if necessary |
| Variation in atmospheric pressure | Shifts converted absolute pressure | Results vary with day or measurement time | Use atmospheric pressure measured at the time of the experiment |
| Deviation from ideal-gas behavior | Intermolecular forces and molecular volume can no longer be neglected | Deviation increases at high pressure and low temperature | Measure at low pressure and near room temperature |
| Thermal expansion of the container | The container volume itself changes | Contributes to the volume change in Charles’s law | Correct for container expansion |
| Timing of recording measurements | Values are recorded before equilibrium | Reproducibility worsens even under the same conditions | Record only after pressure, temperature, and volume stabilize |
Why Pressure and Volume Are Inversely Proportional in Boyle’s Law
At constant temperature, the average kinetic energy of gas molecules is approximately constant. Decreasing the volume increases the frequency with which molecules collide with the container walls, thereby increasing the pressure.
Why Volume and Absolute Temperature Are Proportional in Charles’s Law
When temperature is increased while pressure is held constant, gas molecules move more vigorously. To maintain constant pressure, the container volume must increase so that the collision frequency with the walls is adjusted.
Why Absolute Temperature Is Used Instead of Celsius Temperature
The thermal motion of gas molecules corresponds to absolute temperature. Molecular motion does not disappear at 0 °C, so Celsius temperature cannot be used directly in a proportional relationship.
Why a Graph of Pressure Versus 1/V Is Linear
From Boyle’s law, when temperature and amount of gas are constant, P = constant × 1/V. Therefore, plotting pressure on the vertical axis and 1/V on the horizontal axis produces a straight line passing near the origin.
Why a Graph of Volume Versus Absolute Temperature Is Linear
From Charles’s law, when pressure and amount of gas are constant, V = constant × T. Therefore, plotting volume on the vertical axis and absolute temperature on the horizontal axis produces a straight line passing near the origin.
Example of How to Write the Results
For a fixed amount of air, the relationship between pressure and volume was measured at 25.0 °C. When the absolute pressure was varied from 80.0 to 200.0 kPa, the volume decreased from 63.2 mL to 25.2 mL as pressure increased.
PV at each measurement point ranged from 5040 to 5058 kPa·mL and was nearly constant. This confirmed that pressure and volume are inversely proportional at constant temperature, consistent with Boyle’s law.
In addition, when the temperature was varied from 283.15 to 353.15 K at a pressure of 101.3 kPa, the volume increased from 47.5 mL to 59.3 mL. V/T at each point was nearly constant at approximately 0.168 mL/K, confirming Charles’s law.
Points to Connect the Results to the Discussion
- Was PV constant under constant-temperature conditions?
- Was the relationship between pressure and 1/V linear?
- Was V/T constant under constant-pressure conditions?
- Was the relationship between volume and absolute temperature linear?
- Was PV/T constant in each state?
- Was gauge pressure correctly converted to absolute pressure?
- Was Celsius temperature correctly converted to absolute temperature?
- Were compression and expansion performed slowly?
- Did the gas reach thermal equilibrium with the constant-temperature bath?
- Was there any gas leakage?
- Could dead volume in the syringe and connecting tubing be neglected?
- Was there hysteresis due to piston friction?
- Was there deviation from ideal-gas behavior at high pressure or low temperature?
Discussion Example
In this experiment, the relationships among pressure, volume, and temperature were measured for a fixed amount of air to examine Boyle’s law, Charles’s law, and the Boyle–Charles law.
First, while the temperature was maintained at 25.0 °C, the absolute pressure was varied from 80.0 to 200.0 kPa. The volume decreased as the pressure increased.
PV at each measurement point ranged from 5040 to 5058 kPa·mL and was nearly constant. Therefore, Boyle’s law, which states that pressure and volume are inversely proportional when temperature and amount of gas are constant, was approximately satisfied.
A direct graph of pressure versus volume is curved, whereas a graph of pressure versus 1/V was approximately linear. This is because Boyle’s law states that P is proportional to 1/V.
Next, while pressure was maintained at 101.3 kPa, temperature was varied from 283.15 to 353.15 K. The volume increased as absolute temperature increased.
V/T at each measurement point was nearly constant at approximately 0.168 mL/K, confirming Charles’s law, which states that volume is proportional to absolute temperature when pressure and amount of gas are constant.
When the relationship between temperature and volume is expressed using Celsius temperature, the graph does not pass through the origin. This is because gas molecules still undergo thermal motion at 0 °C and the gas volume does not become zero. By using absolute temperature, the ideal proportional relationship between volume and temperature can be represented as a straight line through the origin.
Furthermore, when PV/T was calculated under conditions where pressure, volume, and temperature all changed, it was approximately 17.28 kPa·mL/K in each state. This result confirms the Boyle–Charles law.
One source of error in the Boyle’s law measurement is the temperature rise that occurs when a gas is compressed rapidly. Rapid compression temporarily raises the gas temperature, violating the constant-temperature condition and potentially producing a pressure higher than the theoretical value.
To reduce this effect, the piston should be moved slowly, and volume should be recorded only after pressure and temperature have stabilized.
Friction in the syringe piston can also prevent the internal and external pressures from becoming exactly equal. If measurements differ between compression and expansion, hysteresis caused by friction may be present.
In the Charles’s law measurement, if volume is read before the gas reaches the temperature of the constant-temperature bath, the actual gas temperature and thermometer reading will not agree. Therefore, sufficient time should be allowed at each temperature and measurements should be taken only after the volume stabilizes.
When handling pressure data, it is important to add atmospheric pressure to the gauge pressure and convert it to absolute pressure. Using gauge pressure directly causes a large error, particularly at pressures near atmospheric pressure.
For volume measurements, gas is present not only in the graduated syringe but also inside the tubing and pressure sensor. Ignoring this dead volume underestimates the actual gas volume and can prevent PV or V/T from remaining constant.
If gas leaks, the amount of gas changes during the measurement and the Boyle–Charles law can no longer be applied. Connections should be sealed securely, and pressure retention should be checked before and after measurement.
Measurement accuracy can be improved by calibrating the pressure-sensor zero point, operating the apparatus slowly, waiting for the gas to reach thermal equilibrium, correcting for dead volume, and repeating measurements to obtain average values.
In summary, for a fixed amount of air, PV was approximately constant at constant temperature, V/T was approximately constant at constant pressure, and PV/T was approximately constant during general changes of state. Deviations in the measurements may have been caused by temperature changes, gas leakage, piston friction, dead volume, and incorrect conversion of pressure or temperature.
Discussion Example When PV Was Not Constant
Possible reasons why PV was not constant include changes in gas temperature during compression or expansion, gas leakage, failure of internal and external pressures to match because of piston friction, and neglect of dead volume in the connecting tubing.
Discussion Example When V/T Was Not Constant
Possible reasons why V/T was not constant include using Celsius temperature directly, measuring before the gas reached thermal equilibrium with the constant-temperature bath, failure to maintain constant pressure, and neglecting thermal expansion of the container itself.
Discussion Example When Compression and Expansion Gave Different Values
Differences between measurements during compression and expansion may have been caused by piston friction, temporary changes in gas temperature, or differences in the waiting time before readings were taken. The direction of operation and waiting time should be standardized, and measurements should be recorded only after sufficient equilibrium is reached.
Discussion Example When Results Deviated from Theory at High Pressure
Deviation from theoretical values at high pressure may occur because the finite volume of gas molecules and intermolecular forces can no longer be neglected, increasing deviation from ideal-gas behavior. In addition, at small volumes, dead volume and scale-reading errors represent a larger fraction of the total volume.
Summary
According to Boyle’s law, at constant temperature the product PV of gas pressure and volume is constant.
According to Charles’s law, at constant pressure the ratio V/T of gas volume to absolute temperature is constant.
The Boyle–Charles law combines these relationships and states that PV/T is constant for a fixed amount of gas.
In the discussion, it is important to relate the use of absolute pressure and absolute temperature, temperature changes during compression, gas leakage, piston friction, dead volume, and thermal equilibrium to how the measured values deviated from the theoretically constant quantities.
