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

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

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kritika · Answer 1 · 2021-12-29T05:59:36+0000

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

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

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