New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Properties of Matter question

2022 · Shift 2 · Q47

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Advanced
Physics
Properties of Matter
2022 · Shift 2 · Q47

Properties of Matter question

2022 · Shift 2 · Q47

JEE AdvancedPhysicsProperties of MatterMultiple correct+4 / −2

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?

A
If the surface of the bubble is a perfect heat insulator, then $\left(\frac{r_{1}}{r_{2}}\right)^{5}=\frac{P_{a 2}+\frac{2 S}{r_{2}}}{P_{a 1}+\frac{2 S}{r_{1}}}$ .
B
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.
C
If the surface of the bubble is a perfect heat conductor and the change in atmospheric temperature is negligible, then $\left(\frac{r_{1}}{r_{2}}\right)^{3}=\frac{P_{a 2}+\frac{4 S}{r_{2}}}{P_{a 1}+\frac{4 S}{r_{1}}}$ .
D
If the surface of the bubble is a perfect heat insulator, then $\left(\frac{T_{2}}{T_{1}}\right)^{\frac{5}{2}}=\frac{P_{a 2}+\frac{4 S}{r_{2}}}{P_{a 1}+\frac{4 S}{r_{1}}}$ .

More from Properties of Matter

A cylindrical tube, with its base as shown in the figure, is filled with water. It is moving down with a constant acceleration a along a fixed inclined plane with angle $θ$ = 45 $^{\circ}$ . P1 and P2 are pressures at points 1 and 2,… Includes diagram2021 · Multiple correct
As shown schematically in the figure, two vessels contain water solutions (at temperature T) of potassium permanganate (KMnO4) of different concentrations n1 and n2 (n1 > n2) molecules per unit volume with $Δ$ n = (n1 − n2)… Includes diagram2020 · Multiple correct
When water is filled carefully in a glass, one can fill it to a height h above the rim of the glass due to the surface tension of water. To calculate h just before water starts flowing, model the shape of the water above the rim as a disc… Includes diagram2020 · Numerical
An open-ended U-tube of uniform cross-sectional area contains water (density 103 kg m−3 ). Initially the water level stands at 0.29 m from the bottom in each arm. Kerosene oil (a water-immiscible liquid) of density 800 kg m−3 is added to… Includes diagram2020 · MCQ
A train with cross-sectional area St is moving with speed vt inside a long tunnel of cross-sectional area S0 (S0 = 4St). Assume that almost all the air (density $ρ$ ) in front of the train flows back between its sides and the walls of…2020 · Numerical
A hot air balloon is carrying some passengers, and a few sandbags of mass 1 kg each so that its total mass is 480 kg. Its effective volume giving the balloon its buoyancy is V. The balloon is floating at an equilibrium height of 100 m.…2020 · Numerical
A cubical solid aluminium (bulk modulus = $- V \frac{d P}{d V} = 70 GP a$ ) block has an edge length of 1 m on the surface of the earth. It is kept on the floor of a 5 km deep ocean. Taking the average density of water and the acceleration…2020 · Numerical
A current carrying wire heats a metal rod. The wire provides a constant power (P) to the rod. The metal rod is enclosed in an insulated container. It is observed that the temperature (T) in the metal rod changes with time (t) as $T (t) = T_{0} (1 + β t^{\frac{1}{4}})$ …2019 · MCQ