In a particular set of experimental trials, students examine a system described by the equation

QΔt=kπd2(ThTc)4L\frac{Q}{\Delta t}=\frac{k \pi d^2\left(T_h-T_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 dd and Δt\Delta t are constant. (a) If dd is made three times larger, does the equation predict that Δt\Delta t will get larger or smaller? By what factor?


Answered 7 months ago
Answered 7 months ago
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We are given:

  • QΔt=kπd2(ThTe)4L\dfrac{Q}{\Delta t}=\dfrac{k \pi d^2 (T_h-T_e)}{4L} - given expression

  • Constants{Q,k,π,L,Th,Te{\text{Constants}} \Rightarrow\begin{cases} Q, k, \pi,L, T_h , T_e \end{cases}

  • Variables{d,Δt{\text{Variables}} \Rightarrow\begin{cases} d , \Delta t \end{cases}


a) For d=3d=3 , Δt=?\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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