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  4. The quantities of heat required to raise the temperature of two solid copper spheres of radii r1 and r2 (r1 = 1.5 r2) through 1 K are in the ratio :

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Q. 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 :

NEETNEET 2020Thermal Properties of Matter

Solution:

Heat supplied $\Delta\,Q =MS\,\Delta\,T$
For same material ‘s’ remains the same
$\Delta\,Q \propto\,M$ and $M=\frac{4}{3}\pi\,r^{3}\,\rho$
$\Rightarrow \frac{\Delta\,Q_{1}}{\Delta\,Q_{2}}$
$=\left(\frac{r_{1}}{r_{2}}\right)^{3}$
$=\left(\frac{1.5}{1}\right)^{3}$
$=\frac{27}{8}$