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A student is investigating how the boiling point of a salt solution varies with pressure.
It is suggested that the relationship between the Celsius temperature $\theta$ at which the water of the solution starts to boil and the air pressure $P$ is
$\theta = k \sigma P^q$
where $\sigma$ is the density of the solution and $k$ and $q$ are constants.
Design a laboratory experiment to test the relationship between $\theta$ and $P$. Explain how your results could be used to determine values for $k$ and $q$.
You should draw a diagram, on page 3, showing the arrangement of your equipment. In your account you should pay particular attention to
• the procedure to be followed,
• the measurements to be taken,
• the control of variables,
• the analysis of the data,
• any safety precautions to be taken.
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A student is investigating the electric potential near a charged metal sphere. The sphere is suspended from the ceiling as shown in Fig. 2.1.
A flame probe is used to measure the potential $V$ at a distance $L$ from the surface of the sphere. The experiment is repeated for different distances from the sphere.
It is suggested that $V$ and $L$ are related by the equation
$$V = \frac{Q}{4\pi\varepsilon_0 (L + a)}$$
where $Q$ is the charge on the sphere, $a$ is the radius of the sphere and $\varepsilon_0$ is the permittivity of free space.
(a) A graph is plotted of $\frac{1}{V}$ on the y-axis against $L$ on the x-axis.
Determine expressions for the gradient and the y-intercept.
gradient = ..........................................................
y-intercept = ...................................................... [1]
(b) Values of $L$ and $V$ are given in Fig. 2.2.
[Table_1]
Calculate and record values of $\frac{1}{V}/10^{-3} \text{V}^{-1}$ in Fig. 2.2.
Include the absolute uncertainties in $\frac{1}{V}$. [2]
(c) (i) Plot a graph of $\frac{1}{V}/10^{-3} \text{V}^{-1}$ against $L/\text{m}$.
Include error bars for $\frac{1}{V}$. [2]
(ii) Draw the straight line of best fit and a worst acceptable straight line on your graph. Both lines should be clearly labelled. [2]
(iii) Determine the gradient of the line of best fit. Include the absolute uncertainty in your answer.
gradient = .......................................................... [2]
(iv) Determine the y-intercept of the line of best fit. Include the absolute uncertainty in your answer.
y-intercept = ...................................................... [2]
(d) (i) Using your answers to (a), (c)(iii) and (c)(iv), determine the values of $a$ and $Q$. Include an appropriate unit for $Q$.
Data: $\varepsilon_0 = 8.85 \times 10^{-12} \text{F} \text{m}^{-1}$.
$a = ...................................................... \text{m}$
$Q = .......................................................$ [3]
(ii) Determine the percentage uncertainty in $a$.
percentage uncertainty in $a = .................................. \%$ [1]
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