Question

As we will see in Chapter 19, the process of thermal conduction of energy into cylindrical blocks of ice is described by the equation LaTeX: \frac{Q}{\Delta t}=\frac{4\pi d^2\left(T_h-T_c\right)}{4L} Q Δ t = 4 π d 2 ( T h − T c ) 4 L For experimental control, in one set of trials all quantities except LaTeX: d d and LaTeX: \Delta t Δ t are constant. (a) If LaTeX: d d is 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: d 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?

Answer 1

  

If all the other quantities except are constant,

(or)

(or)

a)

If is made 3 times larger , then   

That is will get  smaller. gets smaller by a factor of .

b)

The equation predicts that, and are inversely proportional.

c) To get a straight line for the equation of the form

is taken on vertical axis(Y axis) and is taken on horizontal axis(X axis)

d)

For the above expression, slope of the straight line is