Experiment: Pressure and temperature of a fixed mass of gas at constant volume (pressure law)

Aim

To investigate the relationship between the pressure and the temperature of a fixed mass of gas kept at constant volume.

Variables

• Manipulated: Temperature of the gas, θ
• Responding: Pressure of the gas, P
• Constant: Volume and the mass of the trapped gas

Apparatus & materials

• Round-bottomed flask of dry air
• Bourdon pressure gauge
• Beaker of water
• Thermometer
• Stirrer
• Bunsen burner or hotplate
• Short connecting tube
• Retort stand

Procedure

1. Connect the flask of dry air to the Bourdon gauge with a short tube, and immerse the flask fully in a beaker of water.
2. Stir the water and record the temperature θ and the gauge pressure P when they are steady.
3. Heat the water gently, stirring all the time.
4. At each of several temperatures, stop heating, stir, and record θ and P.
5. Allow time for the air in the flask to reach the water temperature before each reading.
6. Record θ and P for each temperature.

Tabulating results

Record the temperature θ in °C and the gas pressure P (e.g. in kPa). You may add a column for the absolute temperature T in K (T = θ + 273).

The graph

Plot P (y-axis) against temperature θ in °C (x-axis). The straight line, extended back to P = 0, cuts the temperature axis near −273 °C (absolute zero).

Analysis

At constant volume the pressure is directly proportional to the absolute (kelvin) temperature, so P / T = constant. Extrapolating the line to zero pressure gives absolute zero at about −273 °C.

Heat · Graph skills

Sample results and what they show

These are example readings for a fixed mass of dry air in a flask of constant volume, connected to a Bourdon gauge.

• θ = 30 °C, P = 101 kPa
• θ = 40 °C, P = 104 kPa
• θ = 50 °C, P = 108 kPa
• θ = 60 °C, P = 111 kPa
• θ = 70 °C, P = 114 kPa

The pressure climbs steadily as the water bath heats the flask, gaining roughly 3.3 kPa for every 10 °C rise. The volume is fixed, so the faster, harder collisions of the hotter air molecules with the flask walls raise the pressure.

Adding 273 to each Celsius value to get the absolute temperature T shows that P/T stays almost constant, about 0.33 kPa K⁻¹ each time. That constant ratio is the point of the experiment: at constant volume the pressure is proportional to the absolute temperature.

The pressure does not double when θ doubles in °C, which is why temperatures must be converted to kelvin.

Reading the graph and finding the answer

Plot P on the y-axis against θ in °C on the x-axis. The points give a straight line with a positive gradient that does not pass through the origin.

Use a large triangle on the best-fit line, taking two widely spaced points such as (30 °C, 101 kPa) and (70 °C, 114 kPa):

• gradient = (114 − 101) kPa ÷ (70 − 30) °C = 13 kPa ÷ 40 °C = 0.33 kPa °C⁻¹

The gradient is the rise in pressure per degree. Extend the line back until P = 0; it meets the temperature axis at about −273 °C, which is absolute zero.

This confirms P/T = constant. The SPM Physics 4531 papers carry no formula sheet, so recall the pressure-law relationship P/T = constant from memory when you write your conclusion.

Choose axis scales that spread the plotted points across more than half of the grid, and draw the best-fit line so the points are balanced evenly on both sides of it. If one point is clearly off the line, treat it as an anomalous reading, ring it, and leave it out when drawing the line and taking the gradient.

Marks examiners look for

Precautions that keep the result trustworthy:

• Stir the water so the whole bath is at one temperature.
• Wait for the air in the flask to reach the water temperature before each reading.
• Use a short connecting tube so the gas volume stays constant.
• Immerse the flask fully so all the trapped air is heated evenly.

For the Paper-3 science process skills, examiners reward: naming the manipulated variable (θ), responding variable (P) and constants (volume and mass of gas); a table with unit headings and consistent decimals; five or more plotted points with labelled axes and a best-fit line; and a large gradient triangle. State the relationship in words, that pressure rises linearly with temperature, and use the backward extrapolation to about −273 °C as the conclusion that supports absolute zero.

Repeat each reading and take the average to reduce random error, and quote the final answer to a sensible number of significant figures with its correct unit. In the discussion, name one source of error together with a matching improvement, and note that any point off the line was ignored so the conclusion rests on consistent data.

Source: DSKP KSSM Physics Form 4 and 5 (Versi English) (Bahagian Pembangunan Kurikulum (BPK), KPM)