Question 1 :
The root mean square speed of the molecules of a diatomic gas is v. When the temperature is doubled, the molecules dissociate into two atoms. The new root mean square speed of the atom is -
Question 2 : In the adjacent figure one mole of a monoatomic gas is enclosed in an adiabatic vessel by means of a tightly fitted cork. Heat is supplied to the gas at a constant rate Q = 4.5 × 10<sup>-2</sup> J/s, by an electric heater. At time t = 0, temperature of the gas is 27<sup>0</sup>C and its pressure is equal to atmospheric pressure P<sub>0</sub> = 10<sup>5</sup> Pa. If maximum frictional force offered to the cork by the walls of the vessel is 50 N, the time when cork will come out of the vessel is. (The cross-sectional area of the vessel A = 10<sup>-2 </sup>m<sup>2</sup>. Take R = 8.3 J/mol K) -<br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e76e6344389b1556ddf2b27' height='52' width='190' >
Question 3 :
Suppose ideal gas equation {tex} V {/tex} follows {tex} 3VP = constant{/tex}. Initial temperature and volume of the gas are {tex} T {/tex} and {tex} V {/tex} respectively. If gas expand to {tex} 27\ V {/tex} then its temperature will be come
Question 4 :
The mean square speed of 4 molecules of a gas having speeds 1, 2, 3 and 4 m/s is -
Question 5 :
The density of air at a pressure of 10<sup>5</sup> Nm<sup>-2</sup> is 1.2 kgm<sup>-3</sup>. Under these conditions, the root mean square velocity of the air molecules in ms<sup>-1</sup> is -
Question 6 :
If the masses of all molecules of a gas are halved and their speeds doubled, then the ratio of initial and final pressures would be -
Question 7 : Volume versus temperature graph of two moles of helium gas is as shown in figure. The ratio of heat absorbed and the work done by the gas in process 1-2 is -<br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e76e5dfb5f89758f2d519b8' height='130' width='132' >
Question 8 : A partition divides a container having insulated walls into two compartments I and II. The same gas fills the two compartments (shown in figure). The ratio of the number of molecules in compartments I and II is- <br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e76e6844389b1556ddf2bcc' height='75' width='212' >
Question 9 :
When the temperature of a gas is raised from {tex} 27 ^ { \circ } \mathrm { C } {/tex} to {tex} 90 ^ { \circ } \mathrm { C } , {/tex} the percentage increase in the {tex} r . m .s {/tex} velocity of the molecules will be
Question 10 : A certain amount of an ideal gas is taken from state A to state B first along process 1 and then along process 2. If the amount of heat absorbed by the gas is Q<sub>1 </sub>and Q<sub>2</sub> respectively then -<br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e76e5edb5f89758f2d519d4' height='92' width='106' >
Question 11 : The expansion of unit mass of a perfect gas at constant pressure is shown in the diagram. Here<br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e76e5bf491ec9580069a8e0' height='109' width='138' >
Question 12 :
The gas in a vessel is subjected to a pressure of 20 atmosphere at a temperature 27<sup>0</sup>C. The pressure of the gas in the vessel after one half of the gas is released from the vessel and the temperature of the remainder is raised by 50<sup>0</sup>C, is -
Question 13 :
A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at 300 K. The ratio of the average rotational kinetic energy per O<sub>2</sub> molecule to per N<sub>2</sub> molecule is-
Question 14 :
The ratio of total K.E. per molecule of O<sub>2</sub> and He at same temperature is -
Question 15 :
If R is universal gas constant, the amount of heat needed to raise the temperature of 2 moles of an ideal monoatomic gas from 273 K to 373 K when no work is done is -
Question 16 : Two spherical vessel of equal volume, are connected by a{tex} \ \ n {/tex} arrow tube. The apparatus contains an ideal gas at one atmosphere and {tex} 300 K {/tex}. Now if one vessel is immersed in a bath of constant temperature {tex} 600 K {/tex} and the other in a bath of constant temperature {tex} 300 K {/tex}. Then the common pressure will be<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5dbfd28fe18860128132d072"><br>
Question 17 :
Cooking gas containers are kept in a lorry moving with uniform speed. The temperature of the gas molecules inside will -
Question 18 :
Air is filled at {tex} 60 ^ { \circ } \mathrm { C } {/tex} in a vessel of open mouth. The vessel is heated to a temperature {tex} T {/tex} so that {tex} 1 / 4 \mathrm { th } {/tex} part of air escapes. Assuming the volume of the vessel remaining constant, the value of {tex} T {/tex} is
Question 19 :
A triatomic molecule can be modelled as three rigid sphere joined by three rigid rods forming an triangle. Consider a triatomic gas consisting such molecule. If gas performs 30 J work when it expands under constant pressure the heat given to gas is -
Question 20 :
The {tex} r . m .s {/tex} velocity of a gas at a certain temperature is {tex} \sqrt { 2 } {/tex} times than that of the oxygen molecules at that temperature. The gas can be
Question 21 :
The equation of state for 5 g of oxygen at a pressure P and temperature T, when occupying a volume V, will be (where R is the gas constant)
Question 22 :
If masses of all molecules of a gas are halved and their speed doubled, then the ratio of initial and final pressure is -
Question 23 :
A cylinder of fixed capacity <b>44.8 litre</b>, contains a monatomic gas at standard temperature and pressure. The amount of heat required to cylinder by {tex} \small 10 ^ { \circ } \mathrm { C } {/tex} will be.
{tex} \small( R = {/tex} universal gas constant)
Question 24 : An air bubble doubles its radius on raising from the bottom of water reservoir to be the surface of water in it. If the atmospheric pressure is equal to {tex} 10 { m } {/tex} of water, the height of water in the reservoir is<br><img style='object-fit:contain' src="https://data-screenshots.sgp1.digitaloceanspaces.com/5dc1643450b49266d2058d77.jpg" />
Question 25 :
Which of the following statement is not a similarity between electrostatic and gravitational forces.?
Question 26 :
Which of the following statements is correct regarding the universal gravitational constant G ?
Question 27 :
If we assume only gravitational attraction between proton (mass <em>M</em>) and electron (mass <em>m</em>) in a hydrogen atom and also assume Bohr’s quantization condition, then the expression for the n<sup>th</sup> orbit energy of the H-atom will be
Question 28 :
A body falls freely under gravity. Its speed is {tex} v {/tex} when it has lost an amount {tex} U {/tex} of the gravitational energy. Then its mass is
Question 29 :
The time period of a satellite of earth is {tex} {5} {/tex} hours. If the separation between the earth and the satellite is increased to four times the previous value, the new time period will become
Question 30 :
The height of the point vertically above the earth's surface, at which acceleration due to gravity becomes {tex} 1 \% {/tex} of its value at the surface is (Radius of the earth {tex} = R ) {/tex}
Question 31 :
When you move from equator to pole, the value of acceleration due to gravity (g)
Question 33 :
{tex}\mathbf {Assertion}{/tex} :The difference in the value of acceleration due to gravity at pole and equator is proportional to square of angular velocity of earth.<br>{tex}\mathbf {Reason}{/tex} : The value of acceleration due to gravity is minimum at the equator and maximum at the pole.
Question 34 :
The ratio of the {tex} K.E. {/tex} required to be given to the satellite to escape earth's gravitational field to the {tex} K.E. {/tex} required to be given so that the satellite moves in a circular orbit just above earth atmosphere is
Question 35 :
A particle of mass {tex} 10 \mathrm { g } {/tex} is kept on the surface of a uniform sphere of mass {tex} 100 \mathrm { kg } {/tex} and radius {tex} 10 \mathrm { cm } . {/tex} Find the work to be done against the gravitational force between them to take the particle far away from the sphere.<br>(you may take {tex} \left. G = 6.67 \times 10 ^ { - 11 } \mathrm { Nm } ^ { 2 } / \mathrm { kg } ^ { 2 } \right) {/tex}<br>
Question 36 :
The weight of body on earth is 60 N. Its weight on moon will be :
Question 37 :
{tex}\mathbf {Assertion}{/tex} : The universal gravitational constant is same as acceleration due to gravity.<br>{tex}\mathbf {Reason}{/tex} : Gravitational constant and acceleration due to gravity have same dimensional formula.<br>
Question 38 :
A point <em>P</em> {tex}\left( R\sqrt{3},\ 0,\ 0 \right){/tex} lies on the axis of a ring of mass <em>M</em> and radius <em>R</em>. The ring is located in <em>y</em>-<em>z</em> plane with its centre at origin <em>O</em>. A small particle of mass <em>m</em> starts from <em>P</em> and reaches <em>O</em> under gravitational attraction only. Its speed at <em>O</em> will be
Question 39 : The planet is revolving around the sun as shown in elliptical path. The correct option is <br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e7615f44389b1556ddf1dfd' height='102' width='159' >
Question 40 :
Assertion: When a soda water bottle falls freely from a height $h$, the gas bubble rises in water from the bottom
Reason: Air is lighter than liquid
Question 41 :
The force of attraction between a hollow spherical shell of uniform density and a point mass situated outside is just as if the entire mass of the shell is
Question 42 :
<font>Two satellites S and S' revolve around the earth at distances 3R and 6R from the centre of the earth. Their periods of revolution will be in the ratio :</font></p>
Question 43 :
<font>The time period of a satellite of Earth is 5 hours. If the separation between the Earth and the satellite is increased to 4 times the previous value, the new time period will become - </font> </p>
Question 44 :
Assertion: First law of thermodynamics is a restatement of the<br>principle of conservation
Reason: Energy is fundamental quantity.
Question 45 :
Air in a cylinder is suddenly compressed by a piston, which is then maintained at the same position. With the passage of time :<br/>
Question 46 :
A gas expands from 40 litres to 90 litres at a constant pressure of 8 atmospheres.Work done by the gas during the expansion is
Question 47 :
During a cyclic thermodynamic process, a gas absorbs 45 J of heat.<br>Which table correctly describes the change in internal energy in the gas and work done by the gas during this cycle?
Question 48 :
For an ideal gas equation of a process for which the heat capacity of the gas varies with temperature as C = $\dfrac { \alpha }{ T }$ ($\alpha$ is a constant) is given by
Question 49 :
A lead bullet (specific heat $=0.32cal.gm^{o}C$) is completely stopped when it strikes a target with a velocity of $300m/s$. The heat generated is equally shared by the bullet and the target. The rise in temperature of bullet will be-
Question 50 :
A perfect gas goes from state A to another state B By absorbing $8 \times 10^{5}$ J of heat and doing $6.5 \times 10^{5}$ J of external work. It is now transfered between the same two states in another process in which it absorbs $10^{5}$ J of heat. then in the second process
Question 51 :
An ideal gas is subjected to a cyclic process involving four thermodynamic states; the amounts of heat (Q) and work (W) involved in each of these states are $Q_1 = 6000 \,J, Q_2 = 5500 \,J, Q_3 = -3000 \,J, Q_4 = 3500 \,J \,W_1 = 2500 \,J, W_2 = -1000 \,J, W_3 = -1200 \,J, W_4 = xJ$. The ratio of the net work done by the gas to the total heat absorbed by the gas in '$\eta$'. The values of $x$ and $\eta$ respectively are:
Question 52 :
The internal energy of a solid also increases when the heat is transferred to its surroundings. A 5 kg solid bar is heated at atmospheric pressure. Its temperature increases from $20^{0}C$ to $70^{0}C$. The linear expansion coefficient of solid bar is $ 1 \times 10^{-3}/C^{0}$. The density of a solid bar is 50 kg/$m^{3}$. The specific heat capacity of a solid bar is 200 J/kg C$^{0}$. The atmospheric pressure is $ 1 \times 10^{5} N/m^{2}$.<br/> The work done by the solid bar due to thermal expansion, under atmospheric pressure, is
Question 55 :
The specific heat of hydrogen gas at constant pressure is $C_{p} = 3.4 \times 10^{3} cal / kg ^{o}C$ and at constant volume is $C_{V} = 2.4 \times 10^{3} cal / kg ^{o}C$ If one kilogram hydrogen gas is heated from $10^{o} C$ to $ 20^{o} C$ at constant pressure, the external work done on the gas to maintain is at constant pressure is
Question 56 :
A thermodynamic process, 200 J of heat is given to a gas and 100 J of work is also done on it. The change in internal energy of the gas is
Question 57 :
A cylinder fitted with a piston contain 0.2 moles of air at temperature $27^{\circ}$. The piston is pushed so slowly that the air within the cylinder remains in thermal equilibrium with the surroundings. Find the approximate work done by the final volume is twice the initial volume
Question 58 :
Assertion: Work and heat are two equivalent from of energy
Reason: Work is the transfer of mechanical energy irrrespective of temperature difference, whereas heat is the transfer of thermal energy because of temperature difference only .
Question 59 :
Which of the following is an example of the first law of thermodynamics ?
Question 60 :
A steel drill is making $180$ Revolutions per minute, under a constant torque of $5 N-m$. If it drills a hole in $7 s$. in a steel block of mass $600 gm$, rise in temperature of the block is $(s= 0.1 cal/gm/ $ <br> ${^ \circ} C$)<br/>
Question 61 : $1\ litre$ of an ideal gas $(\gamma = 1.5)$ at $300\ K$ is suddenly compressed to half its original volume.<br/>If the original pressure is $100\ kPa$, find the work done by the gas in the process .<div>Take: $\sqrt 2=1.41$</div>
Question 62 :
A perfect gas goes from state A to another state B by absorbing $8 \times 10^5J$ of heat and doing $6.5 \times 10^5J$ of external work. It is now transferred between the same two states in another process in which it absorbs $10^5J$ of heat. In the second process
Question 64 :
A thermally insulated rigid container contains an ideal gas. It is heated through a resistance coil of 100$\Omega $ by passing a current of 1 A for five minutes, then change in internal energy of the gas is<br/>
Question 65 :
Consider a rectangular block of wood moving with a velocity $v_0$ in a gas at temperature T and mass density $\rho$. Assume the velocity is along x-axis and the area of cross-section of the block perpendicular to $v_0$ is A. The drag force on the block is (where m is the mass of the gas molecule).
Question 66 :
Two cylinders $A$ and $B$ fitted with pistons contain equal amounts of an ideal diatomic gas at $300\ K$. The piston of $A$ is free to move, while that of $B$ is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $30\ K$, then the rise in temperature of the gas in $B$ is<br>
Question 67 :
An insulated container containing monoatomic gas of molar mass m is moving with a velocity $v_0$. If the container is suddenly stopped. The change in temperature is?
Question 68 :
An iron block of mass $2\;kg$, falls from a height of $10m$. After colliding with the ground it loses $25\%$ energy to surroundings and rest is gained as heat. Then find the temperature rise of the block. (Take sp. heat of iron $470\;J/kg^{\circ}C$)<br/>
Question 69 :
STATEMENT-1: There is a natural asymmetry between converting work to heat and converting heat to work.<br/><br/>STATEMENT-2: No process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work.
Question 70 :
An ideal gas is subjected to cyclic process involving four thermodynamic states, the amounts of heat (Q) and work (W) involved in each of these states are<br>$Q_1\,=\,6000\,J,$<br>$Q_2\,=\,-\,5500\,J;$<br>$Q_3\,=\,-\,3000\,J;$<br>$Q_4\,=\,3500\,J$<br>$W_1\,=\,2500\,J;$<br>$W_2\,=\,-\,1000\,J;$<br>$W_3\,=\,-\,1200\,J;$<br> $W_4\,=\,x\,J.$<br>The ratio of the net work done by the gas to the total heat absorbed by the gas is . The values of $\times$ and $\eta$ respectively are<br>
Question 71 :
Find the external work done by the system inkcal, when 20 keal of heat is supplied to thesystem and the increase in the internal energy is 8400$\mathrm { J } ( \mathrm { J } = 4200 \mathrm { J } / \mathrm { kcal } ) ?$
Question 73 :
In a thermodynamic process pressure of a fixed mass of a gas is changed in such a manner that the gas releases $20J$ of heat and $8J$ of work is done on the gas. If initial internal energy of the gas was $30J$, what will be the fixed internal energy?
Question 75 :
Two cylinders A and B fitted with pistons contain an equal number of moles of an ideal monoatomic gas at $400 K$. The piston of A is free to move while that of B is held fixed. The same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in A is $42 K$, the rise in temperature of the gas in B is
Question 76 :
Two identical containers $ A $ and $ B $ have frictionless pistons. They contain the same volume of an ideal gas at the same temperature. The mass of the gas in $ A $ is $ m_{A} $ and that in $ B $ is $ m_{B} $. The gas in each cylinder is now allowed to expand isothermally to double the initial volume. The change in the pressure in $ A $ and $ B $, respectively, is $ \Delta p $ and $ 1.5 \Delta p $ Then
