MHT CET · Physics · Thermal Properties of Matter
A soap bubble of radius ' \(R\) ' is blown. After heating a solution, a second bubble of radius ' \(2 \mathrm{R}\) ' is blown. The work required to blow the \(2^{\text {nd }}\) bubble in comparison to that required for the \(1^{\text {st }}\) bubble is
- A exactly double.
- B slightly more than 4 times.
- C slightly less than 4 times.
- D slightly less than double.
Answer & Solution
Correct Answer
(C) slightly less than 4 times.
Step-by-step Solution
Detailed explanation
\(\begin{aligned}
\mathrm{W}_1 & =8 \pi \mathrm{R}^2 \mathrm{~T}_1 \\
\mathrm{~W}_2 & =8 \pi(2 \mathrm{R})^2 \mathrm{~T}_2=32 \pi \mathrm{R}^2 \mathrm{~T}_2 \\
\therefore \quad \frac{\mathrm{W}_1}{\mathrm{~W}_2} & =\frac{\mathrm{T}_1}{4 \mathrm{~T}_2}
\end{aligned}\)
When \(\mathrm{T}_1=\mathrm{T}_2, \mathrm{~W}_2=4 \mathrm{~W}_1\)
But as work is done, temperature increases and surface tension decreases.
\(\therefore \quad \mathrm{W}_2 < 4 \mathrm{~W}_1\)
\mathrm{W}_1 & =8 \pi \mathrm{R}^2 \mathrm{~T}_1 \\
\mathrm{~W}_2 & =8 \pi(2 \mathrm{R})^2 \mathrm{~T}_2=32 \pi \mathrm{R}^2 \mathrm{~T}_2 \\
\therefore \quad \frac{\mathrm{W}_1}{\mathrm{~W}_2} & =\frac{\mathrm{T}_1}{4 \mathrm{~T}_2}
\end{aligned}\)
When \(\mathrm{T}_1=\mathrm{T}_2, \mathrm{~W}_2=4 \mathrm{~W}_1\)
But as work is done, temperature increases and surface tension decreases.
\(\therefore \quad \mathrm{W}_2 < 4 \mathrm{~W}_1\)
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