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JEE Advanced (Single Correct MCQs): Heat & Thermodynamics - Airforce X Y / Indian Navy SSR MCQ


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9 Questions MCQ Test Physics for Airmen Group X - JEE Advanced (Single Correct MCQs): Heat & Thermodynamics

JEE Advanced (Single Correct MCQs): Heat & Thermodynamics for Airforce X Y / Indian Navy SSR 2024 is part of Physics for Airmen Group X preparation. The JEE Advanced (Single Correct MCQs): Heat & Thermodynamics questions and answers have been prepared according to the Airforce X Y / Indian Navy SSR exam syllabus.The JEE Advanced (Single Correct MCQs): Heat & Thermodynamics MCQs are made for Airforce X Y / Indian Navy SSR 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for JEE Advanced (Single Correct MCQs): Heat & Thermodynamics below.
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JEE Advanced (Single Correct MCQs): Heat & Thermodynamics - Question 1

A fixed thermally conducting cylinder has a radius R and height L0. The cylinder is open at its bottom and has a small hole at its top. A piston of mass M is held at a distance L from the top surface, as shown in the figure. The atmospheric pressure is P0.

Q.1. The piston is now pulled out slowly and held at a distance 2L from the top. The pressure in the cylinder between its top and the piston will then be

Detailed Solution for JEE Advanced (Single Correct MCQs): Heat & Thermodynamics - Question 1

NOTE : When the piston is pulled out slowly, the pressure drop produced inside the cylinder is almost instantaneously neutralised by the air entering from outside into the cylinder (through the small hole at the top).
Therefore, the pressure inside the cylinder is P0 throughout the slow pulling process.

JEE Advanced (Single Correct MCQs): Heat & Thermodynamics - Question 2

A fixed thermally conducting cylinder has a radius R and height L0. The cylinder is open at its bottom and has a small hole at its top. A piston of mass M is held at a distance L from the top surface, as shown in the figure. The atmospheric pressure is P0.

Q.2. While the piston is at a distance 2L from the top, the hole at the top is sealed. The piston is then released, to a position where it can stay in equilibrium. In this condition, the distance of the piston from the top is

Detailed Solution for JEE Advanced (Single Correct MCQs): Heat & Thermodynamics - Question 2

KEY CONCEPT : The condition for equilibrium of the piston is

Mg = (P0 – p) πR2

NOTE : Since the cylinder is thermally conducting, the temperature  remains the same.
Therefore

 

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JEE Advanced (Single Correct MCQs): Heat & Thermodynamics - Question 3

A fixed thermally conducting cylinder has a radius R and height L0. The cylinder is open at its bottom and has a small hole at its top. A piston of mass M is held at a distance L from the top surface, as shown in the figure. The atmospheric pressure is P0.

Q.3. The piston is taken completely out of the cylinder. The hole at the top is sealed. A water tank is brought below the cylinder and put in a position so that the water surface in the tank is at the same level as the top of the cylinder as shown in the figure. The density of the water is r. In equilibrium, the height H of the water column in the cylinder satisfies

Detailed Solution for JEE Advanced (Single Correct MCQs): Heat & Thermodynamics - Question 3

At equilibrium, p = P

From (i) and (ii)

 

JEE Advanced (Single Correct MCQs): Heat & Thermodynamics - Question 4

A small spherical monoatomic ideal gas bubble (γ = 5/3) is trapped inside a liquid of density ρ (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 T0, the height of the liquid is H and the atmospheric pressure is P0 (Neglect surface tension).

Q.4. As the bubble moves upwards, besides the buoyancy force the following forces are acting on it

 

Detailed Solution for JEE Advanced (Single Correct MCQs): Heat & Thermodynamics - Question 4

The forces acting besides buoyancy force are (a) Force of gravity (vertically downwards) (b) Viscous force (vertically downwards)

JEE Advanced (Single Correct MCQs): Heat & Thermodynamics - Question 5

A small spherical monoatomic ideal gas bubble (γ = 5/3) is trapped inside a liquid of density ρ (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 T0, the height of the liquid is H and the atmospheric pressure is P0 (Neglect surface tension).

Q.5. When the gas bubble is at a height y from the bottom, its temperature is –

Detailed Solution for JEE Advanced (Single Correct MCQs): Heat & Thermodynamics - Question 5

t is given that the bubble does not exchange any heat with the liquid. This means that while the bubble moves up and expand, the process is adiabatic.
For adiabatic expansion the pressure -temperature relationship is

JEE Advanced (Single Correct MCQs): Heat & Thermodynamics - Question 6

A small spherical monoatomic ideal gas bubble (γ = 5/3) is trapped inside a liquid of density ρ (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 T0, the height of the liquid is H and the atmospheric pressure is P0 (Neglect surface tension).

Q.6. The buoyancy force acting on the gas bubble is (Assume R is the universal gas constant)

Detailed Solution for JEE Advanced (Single Correct MCQs): Heat & Thermodynamics - Question 6

Buoyancy force = weight of fluid displaced = (mass of fluid displaced) g

= Vρlg    ...(ii)

where V = Volume of fluid displaced                 = Volume of the bubble.
Now, PV = nRT

Where P is pressure of the bubble at an arbitrary location distant y from the bottom.
Substituting the value of tempertaure from equtaion (i) we get

From (ii) and (iii)

 

 

JEE Advanced (Single Correct MCQs): Heat & Thermodynamics - Question 7

In the figure, a container is shown to have a movable (without friction) piston on top. The container and the piston are all made of perfectly insulated material allowing no heat transfer between outside and inside the container. The container is divided into two compartments by a rigid partition made of a thermally conducting material that allows slow transfer of heat. The lower compartment of the container is filled with 2 moles of an ideal monatomic gas at 700 K and the upper compartment is filled with 2 moles of an ideal diatomic gas at 400 K. The heat capacities per mole of an ideal monatomic gas are  those for an ideal diatomic gas are  

Q.7. Consider the partition to be rigidly fixed so that it does not move. When equilibrium is achieved, the final temperature of the gases will be

 

Detailed Solution for JEE Advanced (Single Correct MCQs): Heat & Thermodynamics - Question 7

Heat lost by monatomic gas at constant volume = Heat gained by diatomic gas at constant pressure

JEE Advanced (Single Correct MCQs): Heat & Thermodynamics - Question 8

In the figure, a container is shown to have a movable (without friction) piston on top. The container and the piston are all made of perfectly insulated material allowing no heat transfer between outside and inside the container. The container is divided into two compartments by a rigid partition made of a thermally conducting material that allows slow transfer of heat. The lower compartment of the container is filled with 2 moles of an ideal monatomic gas at 700 K and the upper compartment is filled with 2 moles of an ideal diatomic gas at 400 K. The heat capacities per mole of an ideal monatomic gas are  those for an ideal diatomic gas are  

Q.8.  Now consider the partition to be free to move without friction so that the pressure of gases in both compartments is the same. The total work done by the gases till the time they achieve equilibrium will be

Detailed Solution for JEE Advanced (Single Correct MCQs): Heat & Thermodynamics - Question 8

In this case both the gases are at constant pressure.

Applying first law of thermodynamics

As the gas two system is thermally insulated, therefore

Therefore, total work done = –100 R

JEE Advanced (Single Correct MCQs): Heat & Thermodynamics - Question 9

Statement-1 : The total translational kinetic energy of all the molecules of a given mass of an ideal gas is 1.5 times the product of its pressure and its volume.  because

Statement-2 : The molecules of a gas collide with each other and the velocities of the molecules change due to the collision.

Detailed Solution for JEE Advanced (Single Correct MCQs): Heat & Thermodynamics - Question 9

Statement 1 : The total kinetic energy of n moles of gas

Statement one is true.
Statement 2 :  The molecules of a gas collide with each other and the velocities of the molecules change due to collision.
But statement 2 is not a correct explanation of statement 1.

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