Kinetic Theory of Gases
- 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 After some oxygen is withdrawn from the cylinder, its gauge pressure drops to 11 atmospheric pressure at temperature 27^°C. The mass of the oxygen withdrawn from the cylinder is nearly… Answer: 3. 0.116 kg Key idea: use PV=nRT for the gas left, then subtract from the initial moles. The gauge pressure must be converted to abs... 1
- 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… Answer: 2. 1.6 atm Key idea: no heat or work leaves the container, so the total internal energy is conserved. For the same gas, this gives n... 1
- 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: Answer: 1. P₁>P₂>P₃ Key idea: For an ideal gas PV=nRT , so at fixed pressure T=P/nRV : the T-V line has slope P/nR . A larger pressure gives... 1
- The temperature of a gas is -50^° C. To what temperature the gas should be heated so that the rms speed is increased by 3 times? Answer: 3. 3295^° C v_rms∝√(T) . The key reads \"increased by 3 times\" as the speed becoming v+3v=4v . T₁ = -50+273=223 K. v₂/v₁=4⇒ T₂=16T₁... 1
- The volume occupied by the molecules contained in 4.5 kg water at STP, if the intermolecular forces vanish away is : Answer: 1. 5.6 m ³ With intermolecular forces gone, the water molecules behave like an ideal gas, and one mole occupies 22.4 L at STP. Moles... 1
- 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… Answer: 3. (A) - (Q), (B) - (P), (C) - (S), (D) - (R) (A) rms speed =√(3RT/M) matches Q. (B) Pressure =1/3 nmbar v² matches P. (C) Average k... 1
- The average thermal energy for a mono-atomic gas is : (k_B is Boltzmann constant and T, absolute temperature) Answer: 2. 3/2k_BT A monoatomic gas molecule has only 3 translational degrees of freedom. By the equipartition law each gives 1/2k_BT . E=3×... 1
- A cylinder contains hydrogen gas at pressure of 249 kPa and temperature 27^°C.Its density is : (R = 8.3 J mol^-1 K^-1) Answer: 2. 0.2 kg/m ³ Use the ideal gas equation in density form: P=ρ RT/M . M=2×10⁻³ kg/mol, T=300 K, P=2.49×10⁵ Pa. ρ=PM/RT=frac2.49×10⁵×2... 1
- The mean free path for a gas, with molecular diameter d and number density n can be expressed as : Answer: 2. 1/√(2) nπ d² The standard result for the mean free path of a gas is λ=1/sqrt2 nπ d² It falls with number density n (more molecule... 1
- Increase in temperature of a gas filled in a container would lead to : Answer: 2. increase in its kinetic energy The temperature of a gas measures the average kinetic energy of its molecules. Raising the tempera... 1
- 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) = 2.76×10^-26 kgBoltzmann's constant k_B = 1.38×10^-23 J K^-1) Answer: 3. 8.360×10⁴ K The molecules escape only if their rms speed equals the escape speed of the Earth, v_e = 11.2\ mathrmkm s⁻¹ = 1.12×10... 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 : Answer: 3. 11 RT Key idea: internal energy U=f/2nRT . O₂ is diatomic ( f=5 , vibration neglected): U=5/2×2RT=5RT . Ar is monatomic ( f=3 ):... 1
- 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? Answer: 1. Pm/(kT) Density ρ=mass/volume . Use the ideal gas law in terms of the number of molecules N : PV=NkT . Mass =Nm , so ρ=Nm/V=Pm/kT... 1
- The molecules of a given mass of a gas have r.m.s. velocity of 200\ ms^-1 at 27^° C and 1.0×10^5\ Nm^-2 pressure. When the temperature and pressure of the gas are respectively, 127^° C and 0.05×10^5\ Nm^-2, the r.m.s. velocity of its molecules in ms^… Answer: 2. 400/√(3) Key idea: v_rms∝sqrt T ; it does not depend on pressure directly for a fixed gas. v₂/v₁=√(400/300)=2/sqrt3 , so v₂=400/s... 1