Serway & Jewett — Physics and Measurement: Problem 28

Figure P1.28 shows students studying the thermal conduction of energy into cylindrical blocks of ice. As we will see in Chapter 19, this process is described by the equation \[ \frac{Q}{\Delta t} = \frac{k\pi d^2 (T_h - T_c)}{4L} \] For experimental control, in one set of trials 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 get smaller? By what factor? (b) What pattern of proportionality of \(\Delta t\) to \(d\) does the equation predict? (c) To display this proportionality as a straight line on a graph, what quantities should you plot on the horizontal and vertical axes? (d) What expression represents the theoretical slope of this graph?