2020 Thermal Properties of MatterSpecific Heat Capacity and Calorimetry Medium Question 7 of 49 in Thermal Properties of Matter

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:

A $\frac{9}{4}$
B $\frac{3}{2}$
C $\frac{5}{3}$
D $\frac{27}{8}$

The answer is D.

Solution

$\Delta Q = ms\Delta T = \left(\frac{4}{3}\pi r^3\rho\right)s\Delta T$ Same material and same $\Delta T$, so $\Delta Q \propto r^3$ $\frac{\Delta Q_1}{\Delta Q_2} = \left(\frac{r_1}{r_2}\right)^3 = (1.5)^3 = \frac{27}{8}$

Concept heat capacity of spheres of different radii

Thermal Properties of Matter in past papers

49 questions from this chapter have appeared across 25 exam years.