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Question 2
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2 (a)
The diagram above illustrates an experimental set-up for verifying Charles’ law. A uniform capillary tube sealed at one end contains a thread of mercury which traps a column of air inside the tube. The tube and a thermometer were tied to a metre rule and placed in beaker filled with water.
Ice cubes are added to the water to reduce its temperature to a value below the room temperature.
The temperature θ and length L of the trapped air column are then read and recorded.
The beaker is heated and five other values of θ and L were determined.
Fig. 2(a) represents the temperature, θi while
Fig 2 (b) represents the corresponding lengths Li of the trapped air.
Where i = 1,2,3,4,5 and 6
(b).jpg)
- Read and record the values of Li
- Read and record the corresponding values of θi
- Tabulate your readings
- Plot a graph with L on the vertical axis and θ on the horizontal axis starting both axes from the origin (0,0)
- Determine the:
- Slope, s, of the graph;
- Intercept, c, on the horizontal axis.
- State two precautions that are necessary to ensure accurate results when performing this experiment.
(b) (i) Given that L = γθ + 1 where L0 is the length of the air column at θ oC and
L0
the expansivity of the tube is negligible, using your graph, determine the value of γ
(ii) Using the diagram above as a guide, determine the pressure of the gas.
( Atmosphere pressure = 75 cmHg)
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This question is based on Charles’ law was attempted by few candidates. Performance was poor. The major problem was with the reading of the thermometer. Some candidates could not read the number line correctly. For example thermometer reading of 32oC, 41oC, 53oC, 62oC were read as 30.2 oC, 40.1 oC, 50. oC ,3 and 60.2 oC. As also shown in the diagram, candidates were expected to measure the readings of the thermometer directly without making use of any scale conversion. However, some of them used unspecified scale factors to convert the temperature which connote rote learning. Another problem observed was on the graph. Many of the candidates did not plan the horizontal axis scale properly hence they could not extrapolate to get the intercept c on the horizontal axis.
In part(b) many candidates failed to determine the value of R using their graph. Determination of R required the knowledge of straight line equation y = mx + c.
The expected answers are:
- Candidates are expected to read and record six values of θ and L to the required number of decimal places and tolerance.
- Plot six points on graph using reasonable scales on correctly distinguish axes
- Draw line of best fit
- Determine the slope of the graph using large right-angled triangle
- Determination of the intercept γ on the horizontal axis
- State any two of the following precautions
e.g - Water was continuously stirred for even distribution of heat
- Capillary tube was kept vertical throughout the experiment
- Bore of the capillary tube was clean and dry before trapping in air.
- Readings were taken at constant atmosphere pressure
- Avoid parallax error in reading thermometer /metre rule
- Repeated readings (stated)
- Avoid thermometer touching the beaker
The expected answers to part (b) are:
(b) (i) L - γ θ + 1
Lo
L = γLoθ + Lo
Slope = γLo
Intercept on the vertical axis = Lo
γ = Slope
Intercept on vertical axis
Correct substitution
Correct arithmetic
(ii) Gas pressure = difference in height = Atmosphere
= 5 + 75
= 80 cm Hg
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