Home
Class 12
PHYSICS
A small spherical monoatomic ideal gas b...

A small spherical monoatomic ideal gas bubble `(gamma= (5)/(3))` is trapped inside a liquid of density `rho_(l)` (see figure) . Assume that the bubble does not exchange any heat with the liquid. The bubble contains n moles of gas. The temperature of the gas when the bubble is at the bottom is `T_(0)`, the height of the liquid is H and the atmospheric pressure is `P_(0)` (Neglect surface tension).

When the gas bubble is at a height y from the bottom , its temperature is :-

A

`T_(0)((P_(0) + rho_(l)gH)/(P_(0) + rho_(l)gy))^(2//5)`

B

`T_(0)((P_(0) + rho_(l)g(H-y))/(P_(0) + rho_(l)gH))^(2//5)`

C

`T_(0)((P_(0) + rho_(l)gH)/(P_(0) + rho_(l)gy))^(3//5)`

D

`T_(0)((P_(0) + rho_(l)g(H-y))/(P_(0) + rho_(l)gH))^(3//5)`

Text Solution

Verified by Experts

The correct Answer is:
B
`T^(gamma)P^(gamma-1)` = constant `implies T_(2) = T_(1)((P_(2))/(P_(1))^((gamma-1)/(gamma))`
=`T_(0)((P_(0) + rho_(l)g(H-y))/(P_(0) + rho_(l)gH))^(1-(3)/(5)) = T_(0) ((P_(0) + rho_(l)g(H-y))/(P_(0) + rho_(l)gH))^(2//5)`
Promotional Banner

Topper's Solved these Questions

  • GEOMETRICAL OPTICS

    ALLEN|Exercise EXERCISE- 01|45 Videos

  • GEOMETRICAL OPTICS

    ALLEN|Exercise EXERCISE-2|44 Videos

  • GEOMETRICAL OPTICS

    ALLEN|Exercise EXERCISE - 05 (B) (MATCH THE COLUMN)|3 Videos

  • CURRENT ELECTRICITY

    ALLEN|Exercise All Questions|427 Videos

  • GRAVITATION

    ALLEN|Exercise EXERCISE 4|9 Videos

Similar Questions

Explore conceptually related problems

A small spherical monoatomic ideal gas bubble (gamma=5//3) is trapped inside a liquid of density rho (see figure). Assume that the bubble does not exchange any heat with the liquid. The bubble contains n moles of gas. The temperature of the gas when the bubble is at the bottom is T_0 , the height of the liquid is H and the atmospheric pressure P_0 (Neglect surface tension). When the gas bubble is at a height y from the bottom, its temperature is-

A small spherical monoatomic ideal gas bubble (gamma=5//3) is trapped inside a liquid of density rho (see figure). Assume that the bubble does not exchange any heat with the liquid. The bubble contains n moles of gas. The temperature of the gas when the bubble is at the bottom is T_0 , the height of the liquid is H and the atmospheric pressure P_0 (Neglect surface tension). The buyoncy force acting on the gas bubble is (Assume R is the universal gas constant)

A small spherical monoatomic ideal gas bubble (gamma=5//3) is trapped inside a liquid of density rho (see figure). Assume that the bubble does not exchange any heat with the liquid. The bubble contains n moles of gas. The temperature of the gas when the bubble is at the bottom is T_0 , the height of the liquid is H and the atmospheric pressure P_0 (Neglect surface tension). As the bubble moves upwards, besides the buyoncy force the following forces are acting on it

The gas inside a spherical bubble expands uniformly and slowly so that its radius increases from R to 2R . Let the atmospheric pressure be p_(0) and surface tension be S . The work done by the gas in the process is

At the boiling point , bubbles form within the liquid because

An air bubble of radius r in water is at a depth h below the water surface at some instant. If P is atmospheric pressure, d and T are density and surface tension of water respectivley . the pressure inside the bubble will be :

Two spherical bubbles of radii 3 cm and 4cm coalesce to form another spherical bubble. Calculate the surface tension of the bubble. The radius of the bubble formed=4.498 cm and the atmopheric pressure =10^(5) Pa

A small air bubble of radius r in water is at depth h below the water surface. If P_0 is the atmospheric pressure, rho is the density of water and T is the surface tension of water, what is the pressure inside the bubble?

A small air bubble of radius 'r' is at a depth 'h' below the water surface (density of water = rho) . Surface tension of water is T, atmospheric pressure is p_(0) . Find pressure inside the air bubble for the condition r lt lt h