The quantities of heat required to raise the temperature of two solid copper spheres of radii and through 1 K are in the ratio [2020]

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Solution

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 [2020]

1 $\frac{27}{8}$

2 $\frac{9}{4}$

3 $\frac{3}{2}$

4 $\frac{5}{3}$

Ans.
(1)

Heat required, $Δ Q = m s Δ T$

$Δ Q = (V \times ρ) \times s Δ T$

$= \frac{4}{3} π r^{3} ρ \cdot s$ $Δ T$

$\frac{Δ Q_{1}}{Δ Q_{2}} = \frac{r_{1}^{3}}{r_{2}^{3}} = {(\frac{r_{1}}{r_{2}})}^{3} = {(1.5)}^{3} = \frac{27}{8}$

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