Every question from past board papers on Kinetic Theory of Gases, newest paper first. Open any question for its full worked answer.
An oxygen cylinder of volume 30 litre has 18.20 moles of oxygen. After some oxygen is withdrawn from the cylinder, its gauge pressure drops to 11 atmospheric pressure at temperature 27\(^\circ\)C. The mass of the oxygen withdrawn from the cylinder is nearly equal to :
[Given, \(R = \frac{100}{12}\) J mol\(^{-1}\)K\(^{-1}\), and molecular mass of O\(_2\) = 32, 1 atm pressure = \(1.01\times10^5\) N/m]
A container has two chambers of volumes \(V_1 = 2\) litres and \(V_2 = 3\) litres separated by a partition made of a thermal insulator. The chambers contains \(n_1 = 5\) and \(n_2 = 4\) moles of ideal gas at pressures \(p_1 = 1\) atm and \(p_2 = 2\) atm, respectively. When the partition is removed, the mixture attains an equilibrium pressure of :
The following graph represents the T-V curves of an ideal gas (where T is the temperature and V the volume) at three pressures \(P_1\), \(P_2\) and \(P_3\) compared with those of Charles's law represented as dotted lines.
Then the correct relation is:
The temperature of a gas is \(-50^\circ\) C. To what temperature the gas should be heated so that the rms speed is increased by 3 times?
The volume occupied by the molecules contained in 4.5 kg water at STP, if the intermolecular forces vanish away is :
Match Column - I and Column - II and choose the correct match from the given choices.
Column - I: (A) Root mean square speed of gas molecules; (B) Pressure exerted by ideal gas; (C) Average kinetic energy of a molecule; (D) Total internal energy of 1 mole of a diatomic gas
Column - II: (P) \(\frac{1}{3}nm\bar{v}^2\); (Q) \(\sqrt{\frac{3RT}{M}}\); (R) \(\frac{5}{2}RT\); (S) \(\frac{3}{2}k_BT\)
A cylinder contains hydrogen gas at pressure of 249 kPa and temperature \(27^\circ\)C.
Its density is : (R = 8.3 J mol\(^{-1}\) K\(^{-1}\))
The mean free path for a gas, with molecular diameter d and number density n can be expressed as :
The average thermal energy for a mono-atomic gas is : (\(k_B\) is Boltzmann constant and T, absolute temperature)
Increase in temperature of a gas filled in a container would lead to :
At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the Earth's atmosphere ?
(Given :
Mass of oxygen molecule (m) = \(2.76\times10^{-26}\) kg
Boltzmann's constant \(k_B = 1.38\times10^{-23}\) J K\(^{-1}\))
A gas mixture consists of 2 moles of \(O_2\) and 4 moles of Ar at temperature T. Neglecting all vibrational modes, the total internal energy of the system is :
The molecules of a given mass of a gas have r.m.s. velocity of \(200\ ms^{-1}\) at \(27^\circ C\) and \(1.0\times10^{5}\ Nm^{-2}\) pressure. When the temperature and pressure of the gas are respectively, \(127^\circ C\) and \(0.05\times10^{5}\ Nm^{-2}\), the r.m.s. velocity of its molecules in \(ms^{-1}\) is :
A given sample of an ideal gas occupies a volume \(V\) at a pressure \(P\) and absolute temperature \(T\). The mass of each molecule of the gas is \(m\). Which of the following gives the density of the gas?
