Chapter 13: Kinetic Theory

A cubic vessel (with faces horizontal + vertical) contains an ideal gas at NTP. The vessel is being carried by a rocket which is moving at a speed of 500 m/s in the vertical direction. The pressure of the gas inside the vessel as observed by us on the ground

1 mole of an ideal gas is contained in a cubical volume V, ABCDEFGH at 300 K. One face of the cube (EFGH) is made up of a material which totally absorbs any gas molecule incident on it. At any given time,

Boyle’s law is applicable for an

a) adiabatic process

b) isothermal process

c) isobaric process

d) isochoric process

A cylinder containing an ideal gas is in a vertical position and has a piston of mass M that is able to move up or down without friction. If the temperature is increased,

a) both p and V of the gas will change

b) only p will increase according to Charle’s law

c) V will change but not p

d) p will change but not V

Volume versus temperature graphs for a given mass of an ideal gas are shown in the figure at two different values of constant pressure. What can be inferred about the relation between P₁ and P₂?

a) P₁ > P₂

b) P₁ = P₂

c) P₁ < P₂

d) data is insufficient

1 mole of H2 gas is contained in a box of volume V = 1.00 m3 at T = 300 K. The gas is heated to a temperature of T = 3000 K and the gas gets converted to a gas of hydrogen atoms. The final pressure would be

a) same as the pressure initially

b) 2 times the pressure initially

c) 10 times the pressure initially

d) 20 times the pressure initially

A vessel of volume V contains a mixture of 1 mole of hydrogen and 1 mole of oxygen. Let f₁(v)dv, denote the fraction of molecules with speed between v and (v + dv) with f₂(v)dv similarly for oxygen. Then

a) f₁(v) + f₂(v) = f(v) obeys the Maxwell’s distribution law

b) f₁(v), f₂(v) will obey the Maxwell’s distribution law separately

c) neither f₁(v) nor f₂(v) will obey the Maxwell’s distribution law

d) f₂(v) and f₁(v) will be the same

An inflated rubber balloon contains one mole of an ideal gas, has a pressure p, volume V, and temperature T. If the temperature rises to 1.1T and the volume is increased to 1.05V, the final pressure will be

a) 1.1 p

b) p

c) less than p

d) between p and 1.1

ABCDEFGH is a hollow cube made of an insulator. Face ABCD has a positive charge on it. Inside the cube, we have ionized hydrogen. The usual kinetic theory expression for pressure

a) will be valid

b) will not be valid since the ions would experience forces other than due to collision with the walls

c) will not be valid since collisions with walls would not be elastic

d) will not be valid because isotropy is lost

Diatomic molecules like hydrogen have energies due to both translational as well as rotational motion. From the equation in kinetic theory pV = 2/3 E, E is

a) the total energy per unit volume

d) only the translational part of energy because rotational energy is very small compared to the translational energy

c) only the translational part of the energy because during collisions with the wall pressure relates to change in linear momentum

d) the translational part of the energy, because rotational energies of molecules can be either sign and its average over all the molecules is zero