First slide

Heat capacity

Question

The quantities of heat required to raise the temperature of two solid copper spheres of radii $r_{1}$ and $r_{2} (r_{1} = 1.5 r_{2})$ through 1 K are in the ratio:

Easy

A

$\frac{9}{4}$
B

$\frac{3}{2}$
C

$\frac{5}{3}$
D

$\frac{27}{8}$

Solution

$\begin{array}{l} Q = msΔt \\ Q \propto r^{3} \\ \frac{Q_{1}}{Q_{2}} = {(\frac{1.5 r_{2}}{r_{2}})}^{3} \\ = \frac{3}{2} x \frac{3}{2} x \frac{3}{2} = \frac{27}{8} \end{array}$

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