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A student is investigating how the rate at which water evaporates varies with temperature. It is suggested that the relationship between the volume of water evaporated per unit time $Y$ and the Celsius temperature $\theta$ of the water is $Y = k\theta^s$ where $k$ and $s$ are constants.
Design a laboratory experiment to test the relationship between $Y$ and $\theta$. Explain how your results could be used to determine values for $k$ and $s$.
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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[15]
549
501
585
A student is investigating the current in a circuit. The circuit is set up as shown in Fig. 2.1.
[Image_1: Figure 2.1, a circuit diagram]
Resistors, each of resistance $R$, are connected in parallel between $P$ and $Q$. The current $I$ is measured. The experiment is repeated for different numbers $n$ of resistors between $P$ and $Q$.
It is suggested that $I$ and $n$ are related by the equation $$E = I \left(\frac{R}{n} + r\right)$$ where $E$ is the electromotive force (e.m.f.) and $r$ is the internal resistance of the power supply.
(a) A graph is plotted of $\frac{1}{I}$ on the $y$-axis against $\frac{1}{n}$ on the $x$-axis.
Determine expressions for the gradient and the $y$-intercept.
gradient = ........................................................
$y$-intercept = ...................................................[1]
(b) Values of $n$, $I$ and $\frac{1}{n}$ are given in Fig. 2.2.
[Table_1: Values of $n$, $I/mA$, $\frac{1}{n}$, $\frac{1}{I}/A^{-1}$]
Calculate and record values of $\frac{1}{I}/A^{-1}$ in Fig. 2.2.
Include the absolute uncertainties in $\frac{1}{I}$. [2]
(c) (i) Plot a graph of $\frac{1}{I}/A^{-1}$ against $\frac{1}{n}$.
Include error bars for $\frac{1}{I}$. [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 $E$ and $r$. Include appropriate units.
Data: $R = 470 \pm 5 \Omega$.
$$E = .................................................................$$
$$r = ...............................................................$$
[3]
(ii) Determine the percentage uncertainty in $r$.
percentage uncertainty in $r$ = ...............................................% [1]
560
532
574
