Solved: The apparatus depicted in the diagram below was used by a student to examine how... [IB Physics (New syllabus)]

Question

SLPaper 2

The apparatus depicted in the diagram below was used by a student to examine how the pressure $p$ of air varies with volume while maintaining a constant temperature.

The air was confined in a tube with a uniform cross-sectional area, positioned above a column of oil.

The pump pushes oil up the tube, reducing the volume of the trapped air.

The student measured the height $H$ of the air column and the corresponding air pressure $p$ . After each decrease in volume, they paused for a while before recording the pressure. Outline why this step was necessary.

[1]

Verified

Solution

in order to keep the temperature constant 1 mark

in to allow the system to reach thermal equilibrium with the surroundings 1 mark

The following graph of $p$ versus $\frac{1}{H}$ was obtained. Error bars were negligibly small.

The equation of the line of best fit is $p = a + \frac{b}{H}$ .

Determine the value of $b$ including an appropriate unit.

[3]

Verified

Solution

recognizes $b$ as gradient 1 mark

calculates $b$ in range $5.8 \times 10^{4}$ to $6.2 \times 10^{4}$ 1 mark

Unit: $\text{Pa m}$ 1 mark

Outline how the results of this experiment are consistent with the ideal gas law at constant temperature.

[2]

Verified

Solution

$V \propto H$ thus ideal gas law gives $p \propto \frac{1}{H}$ 1 mark

so graph should be a straight line through origin, as observed 1 mark

The cross-sectional area of the tube is $1.15 × 10^{-3}$ $\mathrm{m}^2$ and the temperature of air is 295 K. Estimate the number of moles of air in the tube.

[2]

Verified

Solution

$n=\frac{b A}{R T}$ OR correct substitution of one point from the graph 1 mark

$n=\frac{6 \times 10^{4} \times 1.15 \times 10^{-3}}{8.31 \times 295}=0.028 \approx 0.03$ 1 mark

The equation in may be used to predict the pressure of the air at extremely large values of $\frac{1}{H}$ . Suggest why this will be an unreliable estimate of the pressure.

[2]

Verified

Solution

very large $\frac{1}{H}$ means very small volumes / very high pressures 1 mark

at very small volumes the ideal gas does not apply

at very small volumes some of the assumptions of the kinetic theory of gases do not hold 1 mark

The apparatus depicted in the diagram below was used by a student to examine how the pressure

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