Free NEET Physics multiple-choice questions on Pressure & RMS Speed. Attempt each question and reveal the answer with a full explanation.
If the r.m.s. velocity of a gas is v at 27 o C , then its r.m.s. velocity at 627 o C will be: 3 v 3v 2 v 9v The root mean square speed of molecules of an ideal gas at temperature T is v . If the temperature is increased to 4T , the root mean square speed becomes: 2v 4v 2 v v/2 The temperature of a gas is raised from 27 C to 327 C . The root mean square speed of the molecules will increase by a factor of: 2 2 4 3 Which gas will have the highest root mean square velocity at a given temperature? Hydrogen Helium Oxygen Nitrogen The temperature of an ideal gas is increased from 200 K to 800 K . If at 200 K the root mean square velocity of the gas molecules is v , then at 800 K it will be: 2v 4v 2 v v/2 An ideal gas is filled in a closed container and its speed is increased by 2 times. The pressure will become: 4 times 2 times 8 times Remaining same A gas molecule of mass m moving with velocity v collides elastically with the wall of a container. The change in momentum of the molecule is (assume collision normal to the wall): -2mv -mv 0 mv Which of the following speed is the highest for gas molecules at a given temperature? Root mean square speed Average speed Most probable speed They are all equal The molecular weights of two gases are M 1 and M 2 . At temperature T , the ratio of their root mean square speeds is: M 2/M 1 M 1/M 2 M 1/M 2 M 2/M 1 A gas molecule of mass m at temperature T has a root mean square speed v rms . If the mass of the molecule is halved and the temperature is doubled, the new root mean square speed will be: 2v rms v rms 4v rms 2 v rms Which of the following speed distributions has the maximum number of molecules for an ideal gas at a given temperature? Most probable speed Average speed Root mean square speed Velocity of sound in gas Which of the following speed distributions for gas molecules corresponds to the most probable speed ( v mp )? The speed at the peak of the Maxwell-Boltzmann distribution curve The speed where kinetic energy is maximum The arithmetic mean of all speeds The square root of the mean of the squares of speeds What is the percentage increase in the root mean square velocity of a gas if its absolute temperature is increased by 44 % ? 20 % 44 % 22 % 10 % The molar specific heat at constant pressure of an ideal gas is ( 7 2 )R . The ratio of specific heat at constant pressure to that at constant volume is:- 7 5 8 7 5 7 9 7 The molar specific heats of an ideal gas at constant pressure and volume are denoted by C p and C v respectively. If = C p C v and R is the universal gas constant, then C v is equal to 1+ 1- R ( -1) ( -1) R R Increase in temperature of a gas filled in a container would lead to : Decrease in intermolecular distance Increase in its mass Increase in its kinetic energy Decrease in its pressure The average thermal energy for a mono-atomic gas is : ( k B is Boltzmann constant and T, absolute temperature) 3 2 k B T 5 2 k B T 7 2 k B T 1 2 k B T At what temperature is the root mean square speed of molecules of hydrogen gas equal to that of oxygen molecules at 47 C ? 20 K 80 K -253 K 4 K The root mean square speed of the molecules of an enclosed gas is v . If the pressure is doubled keeping the temperature constant, the root mean square speed will be: v 2v v/2 2 v If the pressure of an ideal gas is P and its density is , the root mean square velocity is given by: 3P P 3 3 P 3P The ratio of the most probable speed ( v mp ), the average speed ( v avg ), and the root mean square speed ( v rms ) of molecules in an ideal gas at a constant temperature is given by: 1 : 1.128 : 1.224 1 : 1.224 : 1.128 1.128 : 1 : 1.224 1.224 : 1.128 : 1 Identify the v rms , v avg and v mp on the Maxwell-Boltzmann distribution curve provided below. Peak is v mp , right of peak is v avg , furthest right is v rms . Peak is v rms , right of peak is v avg , furthest right is v mp . Peak is v avg , right of peak is v rms , furthest right is v mp . All three speeds coincide at the peak. A gas at 27 o C has a pressure of 20 Pa and density 1 kg/m 3 . The r.m.s. velocity of the gas molecules is: 60 m/s 20 m/s 10 m/s 20 m/s The speed of sound in a gas is v s and the root mean square speed of the gas molecules is v rms . The ratio v rms /v s is: 3/ /3 3 3/ Calculate the root mean square speed of Helium atoms at 27 C . (Atomic mass of He = 4 u , R = 8.31 J/mol K ): 1367 m/s 430 m/s 900 m/s 2500 m/s At what temperature does the root mean square speed of molecules of an ideal gas become double its value at 27 C ? 927 C 54 C 600 K 108 C Which of the following speed distributions corresponds to a higher temperature? (Consider the Maxwell-Boltzmann distribution curve of dN/dv vs v ) The curve that is flatter and shifted to the right The curve that is taller and shifted to the left The curve that is taller and shifted to the right The curve that is flatter and shifted to the left The ratio of most probable speed to the root mean square speed is: 2/3 3/2 8/3 1:1 A sample of gas is at 0 C . To what temperature must it be raised in order to double the root mean square speed of the molecules? 819 C 273 C 546 C 1092 C A gas is at pressure P . If the masses of all the molecules are made one-third of their original value and their speeds are doubled, then the new pressure will be: 4/3 P 2/3 P 3/4 P 1/3 P At what temperature the molecule of Nitrogen will have the same rms velocity as the molecule of Oxygen at 127 C ? 77 C 350 K 457 K 273 K The molecules of a given mass of a gas have r.m.s velocity of 200 m/s at 27 C and 1.0 10 5 N/m 2 pressure. When the temperature and pressure of the gas are respectively 127 C and 0.05 10 5 N/m 2 , the r.m.s velocity of its molecules in m/s is: 400/ 3 100 2 100/ 2 100 3 Four molecules of a gas have speeds 1, 2, 3 and 4 km/s . The value of the root mean square speed of the gas molecules is: 7.5 km/s 2.5 km/s 10 km/s 3.0 km/s The temperature of a gas is increased from 27 C to 927 C . The root mean square speed will: Become double Become four times Become half Remain same The root mean square velocity of hydrogen molecules at 300 K is 1930 m/s . Then the root mean square velocity of oxygen molecules at 1200 K will be: 965 m/s 1930 m/s 3860 m/s 482.5 m/s The root mean square speed of the molecules of a gas is v at pressure P . If the pressure is increased to 3P while the volume is kept constant, the new root mean square speed will be: 3 v v 3 3v v The ratio of the mean speed to the root mean square speed of molecules of an ideal gas is: 8 3 3 8 2 3 3 2 Which of the following speed distributions correctly describes the behavior of molecules in an ideal gas as temperature increases? The peak of the curve shifts to the right and becomes lower The peak of the curve shifts to the left and becomes higher The peak shifts right and stays at the same height The curve becomes narrower The ratio of most probable speed to average speed is: 4 4 3 2 2 3 A gas is filled in a container at pressure P . If the mass of each molecule is doubled and their RMS speed is halved, the new pressure will be: P/2 P 2P P/4 A mixture of 1 mole of Helium ( M = 4 ) and 1 mole of Methane ( M = 16 ) is kept at a temperature T . The ratio of the root mean square speeds of Helium atoms to Methane molecules is: 2:1 4:1 1:2 1:4 If the absolute temperature of an ideal gas is increased by 1 % , the root mean square speed of the molecules will increase by approximately: 0.5 % 1 % 2 % 0.25 % At a given temperature, which of the following gases will have the lowest most probable speed? CO 2 ( M=44 ) O 2 ( M=32 ) N 2 ( M=28 ) H 2 ( M=2 ) The pressure of an ideal gas is P = 1 3 v rms 2 . This expression is derived by considering: Transfer of momentum to the walls of the container Intermolecular gravitational forces The volume occupied by the molecules Potential energy of the molecules If the pressure of a gas is P and its density is , the root mean square speed is v rms . If the pressure is increased to 2P isothermally, the new root mean square speed is: v rms 2v rms 2 v rms v rms /2 The root mean square velocity of air molecules (average M 29 ) at 0 C is approximately: 485 m/s 330 m/s 150 m/s 1000 m/s The ratio of the root mean square velocity of U 235 F 6 to that of U 238 F 6 at a constant temperature is approximately: 352 349 349 352 352 349 349 352 At what temperature will the root mean square velocity of H 2 be double of its value at 0 C ? 819 C 546 C 273 C 1092 C The root mean square velocity of molecules of a gas is 200 m/s at 27 C . What will be the root mean square velocity at 127 C ? 231 m/s 266 m/s 300 m/s 400 m/s The temperature of a gas is -50 o C . To what temperature should the gas be heated so that its root mean square (r.m.s.) speed is increased by 3 times? 3295 o C 3097 o C 223 o C 669 o C A container has N molecules at temperature T . If the mass of each molecule is doubled and the r.m.s. speed is halved, the pressure of the gas will: Become half Remain the same Become double Become one-fourth The ratio of v rms to the speed of sound v s in a monoatomic gas is: 5/3 3/5 9/5 3 The most probable speed of Oxygen molecules at 300 K is v . What is the most probable speed of Hydrogen molecules at 300 K ? 4v 16v v/4 v/16 At what temperature will the root mean square speed of H 2 molecules be equal to the root mean square speed of O 2 molecules at 400 K ? 25 K 50 K 100 K 12.5 K A gas molecule of mass m strikes a wall with speed v at an angle with the normal and rebounds with the same speed at the same angle. The change in momentum of the molecule is: 2mv 2mv mv Zero In the Maxwell-Boltzmann distribution, if v mp is the most probable speed and v rms is the root mean square speed, then for a gas at a fixed temperature, which is true? v rms > v mp v rms < v mp v rms = v mp v rms = 2 v mp Which of the following speed distributions has the widest peak (broadest curve) for the same gas? Curve at 1000 K Curve at 500 K Curve at 300 K Curve at 100 K The root mean square speed of a gas molecule is v . If the temperature is increased by 300 % , the new root mean square speed will be: 2v 3v 4v 3 v What is the root mean square speed of a molecule with mass 10 -22 g at 27 C ? (Take k B = 1.38 10 -23 J/K) 352.5 m/s 600 m/s 11.2 m/s 3.5 m/s Which of the following speed distributions shifts towards the right and becomes flatter as temperature increases? Maxwell-Boltzmann distribution Planck distribution Bohr distribution Fermi-Dirac distribution A gas molecule of mass m has an average translational kinetic energy E . Its most probable speed is: 4E 3m 2E 3m E m 3E m The amount of heat energy required to raise the temperature of 1 g of Helium at NTP, from T 1 K to T 2 K is 3 8 N a k B (T 2 - T 1) 3 2 N a k B (T 2 - T 1) 3 4 N a k B (T 2 - T 1) 3 4 N a k B ( T 2 T 1 ) Match Column - I and Column - II and array ll Column - I & Column - II (A) Root mean square speed of gas molecules & (P) 1 3 nm v 2 (B) Pressure exerted by ideal gas & (Q) 3 RT M (C) Average kinetic energy of a molecule & (R) 5 2 RT (D) Total internal energy of 1 mole of a diatomic gas & (S) 3 2 k B T array choose the correct match from the given choices. (A) - (Q), (B) - (R), (C) - (S), (D) - (P) (A) - (Q), (B) - (P), (C) - (S), (D) - (R) (A) - (R), (B) - (Q), (C) - (P), (D) - (S) (A) - (R), (B) - (P), (C) - (S), (D) - (Q) At what temperature will the root mean square speed of oxygen molecules ( O 2 ) be sufficient for escaping from the Earth's atmosphere? (Given: Escape velocity v e = 11.2 km/s , Boltzmann constant k B = 1.38 10 -23 J/K , mass of oxygen molecule m = 5.34 10 -26 kg ) 1.6 10 5 K 2.4 10 4 K 5.2 10 3 K 8.1 10 5 K The temperature at which the average translational kinetic energy of a molecule is equal to the energy of a photon of wavelength 600 nm is: ( h = 6.6 10 -34 Js , k B = 1.38 10 -23 J/K ) 1.6 10 5 K 1.6 10 3 K 1.6 10 4 K 1.6 10 2 K A cylinder contains H 2 gas at 27 C and 1 atm pressure. If the RMS speed of the molecules is v , the RMS speed of O 2 molecules at 127 C will be: v 1 12 v 12 v 1 4 v 2 3 The temperature of a gas is increased from 27 C to 127 C . The ratio of the average kinetic energies is: 4:3 3:4 16:9 3 :2 The average kinetic energy of a gas molecule at 300 K is 6.21 10 -21 J . The root mean square speed of the molecule at this temperature (mass m = 10 -26 kg ) is: 1114 m/s 621 m/s 1500 m/s 2000 m/s The root mean square speed of Nitrogen molecules at 27 C is v . If the temperature is increased to 927 C and Nitrogen molecules dissociate into Nitrogen atoms, the new root mean square speed is: 2v 2 2v v 2 4v According to Maxwell's distribution of speeds, as the temperature of a gas increases, the peak of the curve: Shifts to the right and becomes lower Shifts to the left and becomes higher Shifts to the right and becomes higher Shifts to the left and becomes lower A vessel contains 14 g of N 2 gas at temperature 27 C . The amount of heat required to double its v rms speed at constant volume is: 11.25 10 2 R 5.625 10 2 R 22.5 10 2 R 45.0 10 2 R At what temperature will the most probable speed of oxygen molecules ( O 2 ) be equal to the root mean square speed of the same molecules at 27 C ? 177 C 150 C 450 K 600 K If the root mean square speed of H 2 molecules at T 1 is equal to the most probable speed of He atoms at T 2 , the ratio T 1/T 2 is: 1/3 1/4 1/2 1 Identify the correct relationship between the speeds of gas molecules at a given temperature: v rms > v avg > v mp v mp > v avg > v rms v avg > v rms > v mp v rms = v avg = v mp Two gases are at absolute temperatures 300 K and 350 K respectively. The ratio of average kinetic energy per molecule for these two gases is: 6:7 7:6 36:49 49:36