KCET · Physics · Kinetic Theory of Gases
The quantities of heat required to raise the temperatures of two 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 of
- A \(\frac{27}{8}\)
- B \(\frac{9}{4}\)
- C \(\frac{3}{2}\)
- D 1
Answer & Solution
Correct Answer
(B) \(\frac{9}{4}\)
Step-by-step Solution
Detailed explanation
Required heat, \(Q \propto r^{2}\)
where \(r\) is the radius.
\(\therefore \frac{Q_{1}}{Q_{2}} =\frac{r_{1}^{2}}{r_{2}^{2}} \)
\(\frac{Q_{1}}{Q_{2}} =\frac{(1.5)^{2}}{(1)^{2}} \)
\(\frac{Q_{1}}{Q_{2}} =\frac{9}{4}\)
where \(r\) is the radius.
\(\therefore \frac{Q_{1}}{Q_{2}} =\frac{r_{1}^{2}}{r_{2}^{2}} \)
\(\frac{Q_{1}}{Q_{2}} =\frac{(1.5)^{2}}{(1)^{2}} \)
\(\frac{Q_{1}}{Q_{2}} =\frac{9}{4}\)
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