6.2.5

# Boyle's Law & Charles' Law

Test yourself

## Investigation of Boyle's Law

Boyle’s Law describes the relationship between the pressure and volume of a fixed mass of gas at constant temperature.

### Manometer method

• Use a pump to change the air pressure on one side of the manometer.
• Use a pressure gauge on the pump side to measure air pressure, which is equal to the pressure of the air in the glass tube.
• You can measure the volume of trapped air.
• Record the volume for several different pressure values.

### Analysis of manometer method

• If you plot a graph of volume against pressure, you get a monotonically decreasing curve.
• Plot a graph of V-1 against P and the best fit straight line goes through the origin.
• This verifies that V-1 is directly proportional to the pressure, i.e. pV is a constant or that P and V are inversely proportional to each other. This assumes that the temperature and mass of the gas is constant.

### Further analysis of manometer method

• You can use a logarithmic plot.
• Plot log(V) against log (P). It doesn’t matter what base logarithm you use.
• The gradient of the line of best fit should be -1.
• Assume V = k/P where k is a constant.
• log(V) = log(k) - log(P).
• log(V) = - log(P) + log(k).

### Further analysis of manometer method 2

• Compare the last line with y = mx + c.
• If log(V) is plotted on the y-axis, with log(P) on the x-axis, the gradient = -1 and the y-intercept should be log(k).
• You can find the constant, k, using k = Zc, where Z is the base of the logarithms (i.e. 10 or e) and c is the y-intercept.

## Investigation of Boyle's Law 2

Boyle’s Law describes the relationship between the pressure and volume of a fixed mass of gas at constant temperature.

### Syringe and data logging method

• Connect the open end of a syringe to a pressure sensor (which is then connected to data logger and computer).
• Start recording on data logger.
• Move the plunger in steps, i.e. decrease or increase the volume of trapped gas slowly so as not to warm or cool the gas.
• For each new volume, record the pressure.

### Syringe and data logging method 2

• Use software, such as a spreadsheet, to plot a graph of volume against pressure to get a monotonically decreasing curve.
• Use software to plot a graph of V-1 against P.
• The best fit straight line should go through the origin, verifying that V-1 is directly proportional to P.
• i.e. PV = constant or that P and V are inversely proportional to each other, assuming that the temperature and mass of the gas is constant.

## Investigation of Charles’ Law

Charles’ Law describes the relationship between the volume and absolute temperature of a fixed mass of gas at constant pressure.

### Apparatus

• Set up the apparatus as shown in the diagram.
• Caution: it is common practice to use a kerosene-based oil, which needed a separate risk assessment because it is available via CLEAPPS.

### Method

• Keep stirring the water so as to reduce temperature gradients through the water.
• The length of the air column is directly proportional to the volume of trapped air. This assumes that the inner diameter of the capillary tube is constant.

### Analysis

• Plot a graph of the length of air column against temperature on a graph with axes as shown in the diagram.
• I.e. extended back to -400 °C so that an extrapolation back to the temperature axis can give a value for absolute zero.
• Notice that the values of volume and temperature are all bunched to the right.

### Analysis 2

• The extrapolation is suspect because you have to extrapolate a long way before the line hits the temperature axis.
• Repeating this with different gases, different volumes of gas and at different pressures gives different straight lines. All of the best fit straight lines should pass through the same point on the temperature axis.

### Plot the graph again

• If you plot the graph again using the student’s value for absolute zero, the length-temperature graph becomes a straight line through the origin as shown.
• This shows that the volume of gas is directly proportional to the temperature in Kelvin. This assumes that the pressure and mass of the gas are constant.

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