As we will see in Chapter 19, the process of thermal conductionof energy into cylindrical blocks of ice is described by theequation LaTeX: \frac{Q}{\Delta t}=\frac{4\pid^2\left(T_h-T_c\right)}{4L} Q Δ t = 4 π d 2 ( T h − T c ) 4 L Forexperimental control, in one set of trials all quantities exceptLaTeX: d d and LaTeX: \Delta t Δ t are constant. (a) If LaTeX: d dis made three times larger, does the equation predict that LaTeX:\Delta t Δ t will get larger or get smaller? By what factor? (b)What pattern of proportionality of LaTeX: \Delta t Δ t to LaTeX: dd does the equation predict? (c) To display this proportionality asa straight line on a graph, what quantities should you plot on thehorizontal and vertical axes? (d) What expression represents thetheoretical slope of this graph?
