Pressure Of An Ideal Gas - Practice Questions & MCQ

For Brownian motion of particle, match columns I and II.

               Factor                                                                    Effect

     (i) Decrease in size of Brownian particle            (P) Increase of Brownian motion

      (ii) Decrease in density of medium                    (Q) Decrease of Brownian motion

       (iii) Increase in temperature of medium             (R) Unaffected

       (iv) Increase in viscosity of the medium  

  An ideal monoatomic gas is confined in a cylinder by a spring loaded piston of cross-section 8.0 x 10^-3 m². Initially, the gas is at 300K and occupies a volume of 2.4 x 10^-3 m³ and the spring is in its relaxed state as shown in the figure. The gas is heated by a small heater until the piston moves out slowly by 0.1 m. The force constant of the spring is 8000 N/m and the atmospheric pressure is 1.0 x 10⁵ N/m². The cylinder and the piston are thermally insulated.  The piston and the spring are massless and there is no friction between the piston and the cylinder. The final temperature of the gas will be :

(Neglect the heat loss through the lead wires of the heater. The heat capacity of the heater coil is also negligible)

A monoatomic ideal gas is expanded adiabatically to times its initial volume, The ratio of the final rate of collision of molecules with a unit area of container walls to the initial rate will be

A gas at pressure is contained in a vessel. If the masses of all the molecules are halved and their speeds doubled, the resulting pressure would be

The volume V versus temperature T graphs for a certain amount of a perfect gas at two pressures ${\mathrm{P}}_1$ and ${\mathrm{P}}_2$ are shown in the figure. Here

Gas at pressure  is contained in a vessel. If the masses of all the molecules are doubled and their speed is halved, the resulting pressure will be equal to

When an ideal gas at pressure $P$, temperature $T$ and volume $V$ is isothermally compressed to a $V/n$, its pressure becomes ${\mathrm{P}}_{\mathrm{i}}$. If the gas is compressed adiabatically to $\mathrm{V}/\mathrm{n}$, its pressure becomes ${\mathrm{P}}_{\mathrm{a}}$. The ratio ${\mathrm{P}}_{\mathrm{i}}/{\mathrm{P}}_{\mathrm{a}}$ is

An ideal gas is initially at temperature $T$ and volume V . Its volume is increased by $\mathrm{\Delta }\mathrm{V}$ due to an increase in temperature $\mathrm{\Delta }\mathrm{T}$, with pressure remaining constant. The quantity $\delta =\mathrm{\Delta }\mathrm{V}/\mathrm{V}\mathrm{\Delta }\mathrm{T}$ varies with temperature as :

An ideal gas expands isothermally from a volume $V_1$ and $V_2$ and then compressed to original volume $V_1$ adiabatically. Initial pressure is ${\mathrm{P}}_1$ and final pressure is ${\mathrm{P}}_3$. The total work done is W Then:

A cylindrical tube of uniform cross-sectional area $A$ is fitted with two air-tight frictionless pistons. The pistons are connected to each other by a metallic wire. Initially, the pressure of the gas is $P_0$ and temperature is $T_0$, atmospheric pressure is also $P_0$.Now, the temperature of the gas is increased to $2T_0$, the tension of the wire will be