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In a particular set of experimental trials, students examine a system described by the equation
$\frac{Q}{\Delta t}=\frac{k \pi d^2\left(T_hT_c\right)}{4 L}$
We will see this equation and the various quantities in it in Chapter 20. For experimental control, in these vials all quantities except $d$ and $\Delta t$ are constant. (a) If $d$ is made three times larger, does the equation predict that $\Delta t$ will get larger or smaller? By what factor?
Solution
VerifiedWe are given:

$\dfrac{Q}{\Delta t}=\dfrac{k \pi d^2 (T_hT_e)}{4L}$  given expression

${\text{Constants}} \Rightarrow\begin{cases} Q, k, \pi,L, T_h , T_e \end{cases}$

${\text{Variables}} \Rightarrow\begin{cases} d , \Delta t \end{cases}$
Required.
a) For $d=3$ , $\Delta t=?$
b) We are asked to find the pattern of proportionality.
c) We are asked to draw a graph.
d) We are asked to find an equation for the theoretical slope of this graph.
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