A bubble has surface tension S. The ideal gas inside the bubble has ratio of specific heats =5/3 . The bubble is exposed to the atmosphere and it always retains its spherical shape. When the atmospheric pressure is P_{a 1}, the radius of the bubble is found to be r₁ and the temperature of the enclosed gas is T₁. When the atmospheric pressure is P_{a 2}, the radius of the bubble and the temperature of the enclosed gas are r₂ and T₂, respectively. Which of the following statement(s) is(are) correct? [JEE Adv 2022 P2]

If the surface of the bubble is a perfect heat insulator, then ≤ft(r₁/r₂)^5={P_{a 2}+2S/r₂{P_{a 1}+2S/r₁. If the surface of the bubble is a perfect heat insulator, then the total internal energy of the bubble

including its surface energy does not change with the external atmospheric pressure.

If the surface of the bubble is a perfect heat conductor and the change in atmospheric temperature is negligible, then ≤ft(r₁/r₂)³={P_{a 2}+4S/r₂{P_{a 1}+4S/r₁.

If the surface of the bubble is a perfect heat insulator, then ≤ft(T₂/T₁)^{5/2}={P_{a 2}+4S/r₂{P_{a 1}+4S/r₁.

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Properties of Matter

Section: Physics

Question : 5 of 47

Marks: +1, -0

A bubble has surface tension

S

. The ideal gas inside the bubble has ratio of specific heats

\gamma=\frac{5}{3}

. The bubble is exposed to the atmosphere and it always retains its spherical shape. When the atmospheric pressure is

P_{a 1}

, the radius of the bubble is found to be

r_1

and the temperature of the enclosed gas is

T_1

. When the atmospheric pressure is

P_{a 2}

, the radius of the bubble and the temperature of the enclosed gas are

r_2

and

T_2

, respectively.

Which of the following statement(s) is(are) correct?

[JEE Adv 2022 P2]

If the surface of the bubble is a perfect heat insulator, then $\left(\frac{r_1}{r_2}\right)^5=\frac{P_{a 2}+\frac{2S}{r_2}}{P_{a 1}+\frac{2S}{r_1}}$ .
If the surface of the bubble is a perfect heat insulator, then the total internal energy of the bubble
including its surface energy does not change with the external atmospheric pressure.
If the surface of the bubble is a perfect heat conductor and the change in atmospheric temperature is negligible, then $\left(\frac{r_1}{r_2}\right)^3=\frac{P_{a 2}+\frac{4S}{r_2}}{P_{a 1}+\frac{4S}{r_1}}$ .
If the surface of the bubble is a perfect heat insulator, then $\left(\frac{T_2}{T_1}\right)^{\frac{5}{2}}=\frac{P_{a 2}+\frac{4S}{r_2}}{P_{a 1}+\frac{4S}{r_1}}$ .

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