Ideal Gas Equation & Postulates — Practice Questions

Free NEET Physics multiple-choice questions on Ideal Gas Equation & Postulates. Attempt each question and reveal the answer with a full explanation.

A vessel contains 1 mole of O 2 gas at a temperature T . The pressure of the gas is P . An identical vessel contains 1 mole of He gas at a temperature 2T . The pressure of the He gas is: 2P P 4P P/2 For an ideal gas, the slope of the P vs 1/V graph at constant temperature is: nRT -nRT nRT/V -nRT/V 2 At what temperature is the average kinetic energy of a molecule zero? 0 K 0 C -273 C Both 0 K and -273 C An ideal gas has pressure P , volume V , and absolute temperature T . If m is the mass of each molecule and k B is the Boltzmann constant, the density of the gas is given by: Pm k BT PT k Bm Pk B mT m k BTP In the given (V - T) diagram, what is the relation between pressures P 1 and P 2 ? P 2 = P 1 P 2 > P 1 P 2 < P 1 Cannot be predicted The mean free path of molecules of a gas, (radius 'r') is inversely proportional to :- r 3 r 2 r r 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 -1 is : 100 2 400 3 100 2 3 100 3 When the temperature of a gas is raised from 30 C to 90 C , the percentage increase in the r.m.s velocity of the molecules will be : 60 % 10 % 15 % 30 % A gas at 350 K and 15 bar has molar volume 20 percent smaller than that for an ideal gas under the same conditions. The correct option about the gas and its compressibility factor (Z) is : Z < 1 and repulsive forces are dominant Z > 1 and attractive forces are dominant Z > 1 and repulsive forces are dominant Z < 1 and attractive forces are dominant The mean free path for a gas, with molecular diameter d and number density n can be expressed as : 1 2 ,n d 2 1 2 ,n 2 d 2 1 2 ,n 2 2 d 2 1 2 ,n d Choose the correct option for the total pressure (in atm.) in a mixture of 4 g O2 and 2 g H2 confined in a total volume of one litre at 0°C is : [Given R = 0.082 L atm mol -1 K -1 , T = 273 K ] 2.602 25.18 26.02 2.518 The volume occupied by the molecules contained in 4.5 kg water at STP, if the intermolecular forces vanish away is 5.6 10 3 m 3 5.6 10 -3 m 3 5.6 m 3 5.6 10 6 m 3 The internal energy of a system of 1 mole of an ideal gas at temperature T is U . If the gas is diatomic and its temperature is increased to 2T , the internal energy becomes: 2 U 5 U U/2 4 U A 10.0 L flask contains 64 g of oxygen at 27°C. (Assume O2 gas is behaving ideally). The pressure inside the flask in bar is (Given R = 0.0831 L bar K -1 mol -1 ) 498.6 49.8 4.9 2.5 Which amongst the following options are correct graphical representation of Boyle’s law? 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 contain 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 1.8 atm 1.3 atm 1.6 atm 1.4 atm A flask contains argon and chlorine in the ratio of 2 : 1 by mass. The temperature of the mixture is 27 C . The ratio of root mean square speed of the molecules of the two gases ( V rms Ar V rms Cl ) is: (Atomic mass of argon = 40.0 u and molecular mass of chlorine = 70.0 u ) 7 4 2 7 7 2 7 2 Which of the following graphs represents the variation of product PV with pressure P for an ideal gas at constant temperature? A horizontal straight line A straight line passing through origin with positive slope A rectangular hyperbola A parabola 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: 11 RT 15 RT 9 RT 5 RT The density of an ideal gas at pressure P and absolute temperature T is . If the pressure is doubled and the temperature is halved, the new density is: 4 / 4 2 If R is the universal gas constant, the amount of heat required to raise the temperature of 2 moles of an ideal monoatomic gas from 273 K to 373 K when no work is done is: 300 R 150 R 100 R 450 R A container holds 32 g of O 2 at T = 300 K . What is the total translational kinetic energy of the gas? (Given R = 8.31 J/mol K ) 3740 J 1870 J 6230 J 2493 J A cylinder contains 10 kg of gas at a pressure of 10 7 N/m 2 . The amount of gas taken out of the cylinder, if the final pressure is 2.5 10 6 N/m 2 at constant temperature, is: 7.5 kg 2.5 kg 5.0 kg 10.0 kg An ideal gas mixture contains n 1 moles of gas 1 and n 2 moles of gas 2. The pressure of the mixture is P . The ratio of the partial pressure P 1 to the total pressure P is: n 1 / (n 1 + n 2) n 2 / (n 1 + n 2) n 1 / n 2 (n 1 + n 2) / n 1 For an ideal gas, the relation between pressure P and kinetic energy per unit volume E is: P = 2 3 E P = 3 2 E P = 1 3 E P = E Two vessels A and B contain the same ideal gas. The volume of A is twice that of B, and the temperature of A is half that of B. If the number of molecules is the same in both, the ratio of pressures P A/P B is: 1/4 1/2 1 4 If the pressure of an ideal gas is increased by 50 % at constant temperature, the volume will decrease by: 33.3 % 50 % 25 % 66.6 % The kinetic energy per unit mass of an ideal gas at temperature T is: 3RT 2M 3RT 2 3k BT 2m 3RT M Two vessels of volumes V and 2V contain the same ideal gas at pressures P and 2P respectively, and at the same temperature. If the vessels are connected by a tube of negligible volume, the final pressure of the system at the same temperature will be: 5P/3 3P/2 2P 3P If the pressure of a gas is tripled and its absolute temperature is halved, the volume of the gas will change by a factor of: 1/6 6 2/3 3/2 The total kinetic energy of 8 g of methane ( CH 4 ) at temperature T is: (Assume CH 4 is an ideal gas with 6 degrees of freedom) 1.5 RT 3 RT 0.5 RT 6 RT If the mean kinetic energy per unit volume of a gas is E , then the pressure P exerted by the gas is: 2E/3 3E/2 E/3 E/2 For a certain gas, the ratio of specific heats is given to be = 1.5 . For this gas: C V = 2R C V = 3R C P = 3R/2 C V = R/2 What is the average kinetic energy of a Nitrogen molecule at 27 C ? ( k B = 1.38 10 -23 J/K ) 6.21 10 -21 J 4.14 10 -21 J 1.03 10 -20 J 8.28 10 -21 J The ratio of C P/C V for a gas is . The number of degrees of freedom is: 2/( - 1) ( - 1)/2 2/ /2 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 R(T 2 - T 1) 3 2 R(T 2 - T 1) 3 4 R(T 2 - T 1) 3 32 R(T 2 - T 1) A vessel contains O 2 and H 2 in the ratio 1:4 by mass. The ratio of their number of molecules is: 1:64 1:4 1:8 1:16 A gas at 27 C has a volume V and pressure P . On heating, its pressure is doubled and volume is tripled. The resulting temperature will be: 1527 C 1800 C 600 K 327 C If the temperature of a gas is increased by 1 K at constant volume, its pressure increases by 0.4 % . What was the initial temperature of the gas? 250 K 400 K 1000 K 250 C At constant volume, the pressure of a gas is proportional to: Average kinetic energy of molecules Average speed of molecules Root mean square speed of molecules None of these An ideal gas is enclosed in a container at a temperature T . If the container is moving with a constant velocity v , the temperature of the gas will: Remain T Increase Decrease Become zero The kinetic energy of 1 mole of an ideal gas is given by E = 3 2 RT . This energy represents: Translational kinetic energy only Total energy including rotational and vibrational Potential energy of the molecules Energy of the container If f is the number of degrees of freedom of a gas molecule, the ratio of the molar specific heats C P C V is given by: 1 + 2 f 1 + f 2 f f+2 f+2 f-2 For an ideal gas, the value of the adiabatic exponent for a triatomic linear molecule (considering only translational and rotational modes) is: 1.40 1.67 1.33 1.25 The molar heat capacity at constant volume of a mixture of n 1 moles of a monoatomic gas and n 2 moles of a diatomic gas is: 3n 1 + 5n 2 2(n 1 + n 2) R 5n 1 + 3n 2 2(n 1 + n 2) R 3n 1 + 5n 2 2 R n 1 + n 2 2 R For an ideal gas, the number of molecules per unit volume ( n ) is related to the pressure P and absolute temperature T by which of the following relations? ( k B is Boltzmann constant) n = P k B T n = k B T P n = P RT n = RT P The change in internal energy of 2 moles of an ideal monoatomic gas when its temperature is increased by 10 K is: 30R 20R 15R 5R A gas mixture consists of 3 moles of a monoatomic gas and 1 mole of a diatomic gas. The molar heat capacity at constant volume ( C V ) for the mixture is: 1.75R 1.5R 2R 2.5R Ozone ( O 3 ) is a triatomic non-linear molecule. The ratio of its specific heats is: 1.33 1.67 1.40 1.25 What fraction of the total internal energy of a diatomic gas is translational at room temperature? 3/5 2/5 1/3 1/2 Total kinetic energy of 2 g of H 2 gas at 27 C is: 6.23 10 3 J 3.11 10 3 J 1.24 10 4 J 2.08 10 3 J The volume of 1 mole of an ideal gas at 27 C and 1 atm pressure ( 1.013 10 5 Pa ) is approximately: 24.6 L 22.4 L 11.2 L 30.0 L Which of the following graphs of density versus 1/T at constant pressure is a straight line passing through the origin? vs 1/T vs T vs T 2 vs T Calculate the number of moles of an ideal gas in a 5.0 L container at 2 atm and 27 C . ( R = 0.0821 L atm/mol K ) 0.41 0.20 1.22 2.50 A mixture contains 1 mole of Neon ( =1.67 ) and 1 mole of Oxygen ( =1.40 ). The molar heat capacity at constant volume of the mixture is: 2R 1.5R 2.5R 3R According to the kinetic theory of gases, the total translational kinetic energy of 0.5 moles of an ideal gas at 200 K is (take R = 8.31 J/mol K ): 1246.5 J 2493 J 623.25 J 311.6 J A gas is allowed to expand in a vacuum. During this process, the work done by the gas is: Zero Positive Negative Infinite A vessel of volume 10 -3 m 3 contains an ideal gas at 300 K and 10 5 Pa . The number of molecules in the vessel is approximately: 2.4 10 22 6.0 10 23 2.4 10 23 1.2 10 22 The pressure of an ideal gas is written as P = E V where E is the total kinetic energy. What is the value of the proportionality constant for a monoatomic gas? 2/3 1/2 3/2 1/3 The molar heat capacity at constant volume of a mixture of n 1 moles of a monoatomic gas and n 2 moles of a diatomic gas (rigid) is: 3n 1 + 5n 2 2(n 1 + n 2) R 5n 1 + 3n 2 2(n 1 + n 2) R 3n 1 + 5n 2 n 1 + n 2 R n 1 + n 2 2 R Which of the following molecules has the highest number of degrees of freedom at very high temperatures? NH 3 He O 2 CO 2 The kinetic energy of translation of 20 g of Oxygen at 47 C is (molar mass of Oxygen = 32 ): 2493 J 1246 J 3200 J 4700 J The volume of a gas at 20 C is 100 cm 3 at a pressure of 10 5 Pa . If the temperature is raised to 100 C and the pressure is increased to 2 10 5 Pa , what is the final volume? 63.6 cm 3 50.0 cm 3 127.3 cm 3 80.2 cm 3 For a gas mixture of n 1 moles of gas 1 and n 2 moles of gas 2, the adiabatic exponent mix is given by: n 1 C P1 + n 2 C P2 n 1 C V1 + n 2 C V2 n 1 1 + n 2 2 n 1 + n 2 C P1 + C P2 C V1 + C V2 1 2 A vessel contains a mixture of 1 mole of Oxygen and 2 moles of Nitrogen at 300 K . The ratio of the average rotational kinetic energy per O 2 molecule to that per N 2 molecule is: 1:1 1:2 2:1 16:14 A cylinder contains 12 L of Oxygen at 20 o C and 15 atm pressure. If the temperature is raised to 35 o C and the volume is reduced to 8.5 L , the final pressure is approximately: 22.3 atm 30.5 atm 18.2 atm 25.1 atm The partial pressure of O 2 in a mixture of 8 g of O 2 and 14 g of N 2 at a total pressure P is: P/3 P/2 2P/3 P/4 In a gas mixture, the total pressure is the sum of the partial pressures of the individual gases. This law is known as: Dalton's Law Charles's Law Boyle's Law Gay-Lussac's Law A rigid triangular molecule consisting of three identical atoms at its vertices has how many degrees of freedom? 6 3 5 7 What is the total internal energy of 1 gram of Helium at temperature T ? ( M = 4 g/mol ) 3 8 RT 3 2 RT 3RT 3 4 RT The average translational kinetic energy of air molecules at 0 o C is 5.6 10 -21 J . What is its value at 100 o C ? 7.6 10 -21 J 11.2 10 -21 J 5.6 10 -21 J 4.1 10 -21 J A gas mixture consists of 3 moles of Helium and 2 moles of Hydrogen. The effective molar specific heat of the mixture at constant volume C V is: 1.8R 1.5R 2.1R 2.5R Which of the following graphs correctly represents the variation of (P) with (V) for an ideal gas at constant temperature? A straight line with slope -1 A straight line with slope +1 A parabola opening upwards An exponential decay curve A rigid molecule consists of 4 atoms at the corners of a square. The number of degrees of freedom for this molecule at room temperature (neglecting vibrations) is: 6 3 5 7 The molar heat capacity of a gas at constant volume is C V . If the gas is a mixture of 1 mole of monoatomic and 1 mole of diatomic gas, the value of = C P/C V is: 1.50 1.40 1.67 1.33 What is the translational kinetic energy of 1 g of Hydrogen ( M = 2 ) at 127 C ? 2493 J 1246 J 4986 J 3740 J For a gas mixture of n 1 moles of a gas with f 1 degrees of freedom and n 2 moles with f 2 degrees of freedom, the internal energy of the system at temperature T is: RT 2 (n 1f 1 + n 2f 2) RT 2 (f 1 + f 2) (n 1 + n 2) RT 2 (f 1 + f 2) R 2 (n 1f 1 + n 2f 2) At room temperature, the average rotational kinetic energy of a linear triatomic molecule like CO 2 is: k B T 3 2 k B T 1 2 k B T 2k B T A mixture contains 14 g of N 2 and 16 g of O 2 . The total number of moles in the mixture is: 1.0 0.5 2.0 1.5 The number of molecules in 1 cm 3 of an ideal gas at 0 C and 1 atm pressure is called: Loschmidt number Avogadro number Boltzmann constant Universal gas constant A container is filled with 20 g of Argon gas at temperature T . If the temperature is increased by T , the change in internal energy of the gas is: (Molar mass of Argon = 40 g/mol, R is universal gas constant) 3 4 R T 3 2 R T 5 4 R T 5 2 R T A mixture consists of 2 moles of Helium and 2 moles of Hydrogen. The ratio of specific heats for this mixture is: 1.5 1.4 1.67 1.33 If the volume of an ideal gas is doubled and its pressure is halved, what happens to the average translational kinetic energy of its molecules? Remains unchanged It is doubled It is halved It becomes four times The work done by one mole of an ideal gas in an isothermal expansion from volume V 1 to V 2 is: RT (V 2/V 1) RT (V 1/V 2) P(V 2 - V 1) Zero The ratio of rotational kinetic energy to the total internal energy for a rigid diatomic molecule at room temperature is: 2/5 3/5 1/2 2/3 The molar specific heat capacity at constant volume for a certain gas is C V = 5R . This gas is likely: A non-linear polyatomic gas with vibrational modes A monoatomic gas A rigid diatomic gas A linear triatomic gas A gas mixture has = 1.4 . This mixture could be composed of: Two different diatomic gases A monoatomic and a diatomic gas A monoatomic and a triatomic gas Two different monoatomic gases The average translational kinetic energy of a gas molecule in a 2D plane is: k B T 3 2 k B T 1 2 k B T 2 k B T 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 kg Boltzmann's constant k B = 1.38 10 -23 JK -1 ) 5.016 10 4 K 8.360 10 4 K 2.508 10 4 K 1.254 10 4 K For an ideal gas, the graph of P vs 1/V at constant temperature is: A straight line passing through the origin A parabola A rectangular hyperbola A circle 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 ) 0.2 kg/m 3 0.1 kg/m 3 0.02 kg/m 3 0.5 kg/m 3 A mixture of N2 and Ar gases in a cylinder contains 7 g of N2 and 8 g of Ar. If the total pressure of the mixture of the gases in the cylinder is 27 bar, the partial pressure of N2 is : [Use atomic masses (in g mol -1 ) : N = 14, Ar = 40] 12 bar 15 bar 18 bar 9 bar Choose the correct option for graphical representation of Boyle's law, which shows a graph of pressure vs. volume of a gas at different temperatures : 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? 669°C 3295°C 3097 K 223 K 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: P 3 > P 2 > P 1 P 1 > P 3 > P 2 P 2 > P 1 > P 3 P 1 > P 2 > P 3 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 pressures at temperature 27 C . The mass of the oxygen withdrawn from the cylinder is nearly equal to: [Given, R = 100 12 J mol -1 K -1 , and molecular mass of O2 = 32, 1 atm pressure = 1.01 10 5 N/m ] 0.156 kg 0.125 kg 0.144 kg 0.116 kg For a gas mixture of 1 mole of Helium and 1 mole of Nitrogen, the effective value of (ratio of specific heats) is approximately: 1.5 1.4 1.67 1.33 What is the ratio of C p/C v for a gas mixture containing 3 moles of a monoatomic gas and 2 moles of a diatomic gas? 1.53 1.40 1.63 1.33 The number of degrees of freedom for a triatomic linear molecule (like CO 2 ) at high temperatures, including vibrational modes, is: 7 5 6 3 What is the number of degrees of freedom for a rigid diatomic molecule that is constrained to move only in a 2D plane? 3 5 2 4 A cylinder contains 2 moles of gas X at pressure P . If 1 mole of gas Y is added to the cylinder at the same temperature and volume, the new pressure will be: 1.5 P 3 P 2 P P The value of C P - C V for 1 g of Nitrogen gas ( N 2 ) is approximately: (Take R = 8.31 J/mol K ) 0.297 J/g K 8.31 J/g K 28 J/g K 1.4 J/g K A gas mixture consists of 2 moles of He and n moles of H 2 . If the effective value of for the mixture is 19/13 , find the value of n . 4 2 3 5 Calculate the number of molecules in 2 cm 3 of an ideal gas at 27 C and 1.0 10 5 Pa pressure. ( k B = 1.38 10 -23 J/K ) 4.8 10 19 2.4 10 20 1.2 10 21 6.0 10 23 A gas container is moving with a constant velocity v 0 . If the container is suddenly stopped, the increase in temperature of the gas (molar mass M , specific heat capacity C V ) is: M v 0 2 2 C V M v 0 2 C V v 0 2 2 M C V M v 0 2 3 R An ideal gas expands such that PT 2 = constant . The coefficient of volume expansion of the gas is: 3/T 1/T 2/T 4/T A mixture of 1 mole of monoatomic gas and 1 mole of diatomic gas is heated at constant pressure. The ratio of the heat supplied to the increase in internal energy is: 3/2 2/3 5/3 1/2 The molar specific heat at constant volume ( C V ) for a mixture of n 1 moles of a monoatomic gas and n 2 moles of a diatomic gas is: 3n 1 + 5n 2 2(n 1 + n 2) R 5n 1 + 7n 2 2(n 1 + n 2) R n 1 + n 2 2 R 3n 1 + 3n 2 2 R The number of degrees of freedom for a non-linear triatomic molecule at high temperature (where vibrational modes are active) is: 9 6 7 5 For an ideal gas, the thermal expansion coefficient at constant pressure is: 1/T T 1/T 2 Zero A mixture of n 1 moles of Helium and n 2 moles of Hydrogen is taken. If the ratio of specific heats of the mixture is 1.5 , then the ratio n 1:n 2 is: 1:1 2:1 1:2 3:2 Which of the following is true for an ideal gas? There are no intermolecular forces of attraction. The volume of molecules is significant compared to the container volume. Collisions are inelastic. Molecules move in a fixed curved path. Calculate the total kinetic energy of 0.1 moles of Helium gas at 27 C . (Take R = 8.31 J/mol K) 374 J 623 J 249 J 1247 J A mixture of 2 moles of Helium and 4 moles of Nitrogen is kept in a container at 300 K . What is the internal energy of the mixture? (Take R = 8.3 J/mol K ) 32370 J 14940 J 24900 J 37350 J At very high temperature, the molar specific heat at constant volume C V of a diatomic gas like Cl 2 (considering vibrational modes) is: 3.5R 2.5R 1.5R 4.5R Equal moles of hydrogen and oxygen gases are placed in a container with a pin-hole through which both can escape. What fraction of the oxygen escapes in the time required for one-half of the hydrogen to escape ? 1/8 1/4 3/8 1/2 At constant temperature, the product of pressure and volume of a fixed mass of an ideal gas is constant. This is known as: Boyle's Law Charles's Law Gay-Lussac's Law Avogadro's Law The internal energy of an ideal gas is a function of: Temperature only Pressure only Volume only Both pressure and volume A flask of volume V contains gas at pressure P . If half of the gas is removed and the temperature of the remaining gas is doubled, the new pressure is: P 2P P/2 4P Which of the following graphs best represents the variation of pressure P with 1/V for an ideal gas at constant temperature? A straight line passing through the origin. A rectangular hyperbola. A parabola starting from the origin. A horizontal straight line. According to the kinetic theory of gases, at absolute zero temperature: Molecular motion stops. The volume of the gas becomes zero. The pressure of the gas becomes infinite. The molecules break into atoms. Two non-reactive ideal gases are mixed at constant temperature and pressure. The total pressure of the mixture is P . If the number of moles of the two gases are n 1 and n 2 , the partial pressure of the first gas is: n 1 n 1 + n 2 P n 2 n 1 + n 2 P n 1 + n 2 n 1 P n 1 n 2 P A vessel of volume V contains n moles of an ideal gas. If the molecular weight of the gas is M and the mass of a single molecule is m , the density of the gas is: nM/V nm/V M/nV n/MV The degrees of freedom of a triatomic non-linear gas molecule are: 6 3 5 7 Under which of the following conditions does a real gas obey the ideal gas equation PV = nRT most closely? Low pressure and high temperature High pressure and low temperature Low pressure and low temperature High pressure and high temperature At constant temperature, a graph is plotted between PV and P for an ideal gas. The shape of the graph is: A horizontal straight line A straight line passing through the origin A parabola A hyperbola A gas expands in such a way that PV 2 = constant . This gas is: Undergoing a polytropic process. Undergoing an isothermal process. Undergoing an adiabatic process with =2 . Undergoing an isobaric process. The molar specific heat at constant volume C V for a certain ideal gas is 1.5R . If 1 mole of this gas is heated from 300 K to 600 K , the change in internal energy is: 450R 300R 600R 150R The volume of 1 mole of an ideal gas at STP (Standard Temperature and Pressure: 0 C and 1 atm ) is approximately: 22.4 Litres 11.2 Litres 44.8 Litres 1 Litre The average kinetic energy of a gas molecule depends only on its: Absolute Temperature Nature of gas Pressure Volume The value of the Boltzmann constant k B in terms of the Universal Gas Constant R and Avogadro's Number N A is: R/N A N A/R R N A 1/(R N A) A gas at 27 C is heated at constant pressure until its volume is doubled. The final temperature of the gas is: 327 C 54 C 600 C 127 C For a gas with = 1.4 , the number of degrees of freedom is: 5 3 6 7 A cylinder contains N molecules of a gas. If the number of molecules is doubled and the temperature is halved, the pressure becomes: The same Doubled Halved Four times The average kinetic energy of a molecule of a gas at temperature T is E . At temperature 2T , the average kinetic energy will be: 2E 2 E 4E E/2 The average thermal energy for a monoatomic gas is: ( k B is Boltzmann constant and T is absolute temperature) 3 2 k B T 5 2 k B T 1 2 k B T 7 2 k B T The pressure of a gas is increased by 1 % by heating it in a closed vessel. The percentage increase in its temperature is: 1 % 2 % 0.5 % 10 % Which of the following is not an assumption of the kinetic theory of gases? The molecules of a gas exert attractive forces on each other. The volume of the molecules is negligible compared to the volume of the gas. The collisions between molecules are perfectly elastic. The motion of molecules is random. For a diatomic gas at room temperature, the ratio of translational kinetic energy to the total internal energy (neglecting vibrational modes) is: 3/5 2/5 3/7 5/7 The number of molecules per unit volume ( n ) of an ideal gas is given by: P/kT kT/P P/RT RT/P A gas behaves more like an ideal gas at: Low pressure and high temperature High pressure and low temperature Low pressure and low temperature High pressure and high temperature The average velocity of the molecules of an ideal gas in equilibrium is: Zero 8RT/ M 3RT/M 2RT/M A container of volume V contains n 1 moles of gas A and n 2 moles of gas B at temperature T . The total pressure P exerted by the mixture is: (n 1 + n 2)RT/V (n 1/n 2)RT/V (n 1n 2)RT/V (n 1 + n 2)V/RT The degrees of freedom for a polyatomic gas molecule which is non-linear and contains N atoms is (neglecting vibration): 6 3 5 3N The average kinetic energy of a gas molecule is E at 27 C . At what temperature will its average kinetic energy be 2E ? 327 C 54 C 600 C 127 C According to Kinetic Theory of Gases, the pressure exerted by an ideal gas on the walls of a container is due to: Rate of change of momentum of molecules hitting the walls Gravitational pull on the gas molecules Intermolecular attraction between gas molecules Collision between gas molecules themselves Two vessels A and B of equal volume contain the same ideal gas at the same temperature. If the pressure in A is twice that in B, then the ratio of the number of molecules in A to that in B is: 2:1 1:2 1:1 4:1 The work done by a gas in an isobaric process to increase its temperature by T for 1 mole of an ideal gas is: R T 3 2 R T 5 2 R T P V If the number density of an ideal gas is doubled while the temperature is kept constant, the pressure of the gas will: Double Remain unchanged Halve Become four times For a gas having f degrees of freedom, the ratio of specific heats is given by: 1 + 2/f 1 + f/2 f/(f+2) (f+2)/2 A container contains a mixture of 2 g of Hydrogen ( H 2 ) and 16 g of Helium ( He ). The total number of moles in the container is: 5 3 18 9 The compressibility factor Z for an ideal gas is: 1 0 Infinity Variable depending on pressure At constant pressure, which of the following graphs represents the variation of volume V with absolute temperature T for an ideal gas? A straight line passing through the origin A rectangular hyperbola A parabola A horizontal straight line An ideal gas is compressed at constant temperature. During this process, the average kinetic energy of the molecules: Remains the same Increases Decreases First increases then decreases If a gas has n degrees of freedom, the ratio of the specific heats of the gas is: 1 + 2/n 1 + n/2 n/2 (n+1)/n The value of total internal energy for 1 mole of a diatomic gas at temperature T (considering only translational and rotational motion) is: 5 2 RT 3 2 RT 7 2 RT RT Which of the following properties is non-zero for an ideal gas at 0 K ? Volume Pressure Kinetic Energy None of these 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 9/7 8/7 5/7 The ratio of the molar heat capacities C P C V = for a gas is 1.4. The gas is: Diatomic Monoatomic Triatomic linear Triatomic non-linear If the degree of freedom of a gas molecule is f , then the average kinetic energy per molecule is: f 2 k B T f 2 RT 3 2 k B T 1 2 k B T Which of the following is the dimension of the Boltzmann constant? [ML 2T -2 K -1 ] [ML 2T -2 ] [MLT -2 K -1 ] [ML 2T -1 K -1 ] The average kinetic energy of molecules of an ideal gas at temperature T is E . If the temperature is increased to 2T , the average kinetic energy becomes: 2E 2 E 4E E/2 If R is universal gas constant and N A is Avogadro's number, then the number of molecules in 1 cm 3 of an ideal gas at STP is: N A / 22400 22400 N A N A 1/22400 For a gas at a given temperature T , the graph of PV versus P is a horizontal line. This gas is: An ideal gas A real gas at low temperature A real gas at high pressure None of these If the volume of a gas is doubled and its temperature is tripled, the final pressure P 2 in terms of initial pressure P 1 is: 1.5 P 1 3 P 1 0.67 P 1 6 P 1 A polyatomic gas with n degrees of freedom has a molar specific heat capacity at constant volume C V . The value of C P is: n+2 2 R n 2 R n-2 2 R (n+1)R What is the number of degrees of freedom for a non-rigid diatomic molecule? 7 5 3 6 Which of the following graphs correctly represents the variation of the pressure P of an ideal gas with its density at a constant temperature T ? A straight line passing through the origin A parabola A rectangular hyperbola A straight line parallel to the density axis At room temperature, the degrees of freedom for a monoatomic gas, a diatomic gas (rigid), and a non-linear triatomic gas are respectively: 3, 5, 6 3, 5, 5 3, 3, 3 5, 5, 6 A vessel contains 6.023 10 23 molecules of Hydrogen gas. If the volume of the vessel is 22.4 L at 0 o C , the pressure is: 1 atm 2 atm 0.5 atm 22.4 atm A mixture of 1 mole of H 2 and 1 mole of He is taken in a vessel. The ratio of their translational kinetic energies per molecule at the same temperature is: 1:1 2:1 1:2 4:1 An ideal gas at pressure P is compressed until its density is doubled at constant temperature. The new pressure of the gas is: 2P P 2 2 P 4P The average energy per degree of freedom of a gas molecule at temperature T is: 1 2 k B T 3 2 k B T k B T f f 2 k B T A vessel contains 1 mole of gas A (molar mass M ) and 2 moles of gas B (molar mass 2M ) at temperature T . The ratio of the average kinetic energy per molecule of A to that of B is: 1:1 1:2 2:1 1:4 According to the Law of Equipartition of Energy, the molar specific heat at constant volume ( C v ) for a gas with f degrees of freedom is: f 2 R 2 f R ( f 2 + 1)R f R Under what conditions is the behavior of a real gas most similar to that of an ideal gas? Low pressure and high temperature High pressure and low temperature Low pressure and low temperature High pressure and high temperature For a rigid non-linear triatomic molecule, the ratio = C P/C V is: 1.33 1.67 1.40 1.20 The average kinetic energy of a gas molecule at 0 C is E . Its average kinetic energy at 273 C will be: 2E 2 E E 2 4E A real gas behaves as an ideal gas at high temperature because: The kinetic energy of molecules overcomes intermolecular forces The molecules move slower The pressure increases significantly The volume of molecules becomes larger For an ideal gas at a constant pressure, which of the following represents the variation of density with absolute temperature T ? 1/T T T T 2 The total kinetic energy of N molecules of an ideal gas at absolute temperature T is given by E . If the temperature is doubled and the number of molecules is halved, the new total kinetic energy will be: E 2E 0.5E 4E Which of the following graphs represents an isochoric process for an ideal gas? A straight line passing through the origin in a P-T graph A rectangular hyperbola in a P-V graph A horizontal line in a V-T graph A straight line with negative slope in a P-V graph The internal energy of 28 g of N 2 gas at temperature T is (neglecting vibrational modes): 5 2 RT 3 2 RT 7 2 RT 5RT The partial pressure of a gas in a mixture is equal to: Total pressure multiplied by its mole fraction Total pressure divided by its mole fraction Total pressure multiplied by its mass fraction Sum of the pressures of all other gases The value of Boltzmann constant k B is approximately: 1.38 10 -23 J/K 6.63 10 -34 J s 8.31 J/mol K 6.02 10 23 mol -1 The kinetic theory of gases assumes that the collisions between molecules are perfectly elastic. This implies that: Both momentum and kinetic energy are conserved Only momentum is conserved Only kinetic energy is conserved Neither momentum nor kinetic energy is conserved The molar specific heat at constant pressure C p of an ideal gas is (7/2)R . The ratio of specific heats is: 1.4 1.67 1.33 1.2 A gas molecule is constrained to move only along a straight wire (1D motion). The number of degrees of freedom for this molecule is: 1 2 3 5 The term 'gram-molecule' of a gas refers to: One mole of the gas One gram of the gas The mass of one molecule in grams Avogadro number of atoms For different ideal gases at the same temperature, the value of PV/nT : Is the same for all gases Is proportional to the molar mass Is proportional to the degrees of freedom Is zero At absolute zero temperature ( 0 K ), the translational kinetic energy of an ideal gas molecule is: Zero Minimum but non-zero Infinite Equal to its potential energy A container of volume V is divided into two equal parts by a partition. One part contains 1 mole of He and the other contains 1 mole of H 2 at the same temperature T . If the partition is removed, the final pressure is: 2RT/V RT/V 3RT/V RT/2V What is the rotational kinetic energy of 1 mole of a monoatomic gas at temperature T ? Zero 1 2 RT 3 2 RT 5 2 RT The average speed v avg of the molecules of a gas is proportional to: T 1/2 T T 2 T -1/2 A mixture of 2 moles of Helium and 4 moles of Nitrogen is kept in a container. What is the average molar mass of the mixture? 20 g/mol 16 g/mol 14 g/mol 24 g/mol For an ideal gas, which of the following graphs of V vs 1/P at constant temperature is correct? A straight line passing through the origin A rectangular hyperbola A parabola A horizontal straight line The average kinetic energy per degree of freedom for a gas molecule at temperature T is: 1 2 k BT 3 2 k BT k BT f 2 k BT A diatomic gas molecule has 5 degrees of freedom at room temperature. If vibrational modes are excited at high temperature, the number of degrees of freedom becomes 7. What is the ratio of C V at high temperature to C V at room temperature? 7/5 5/7 1/2 9/7 Two gases A and B having molar masses M A and M B are at the same temperature. The ratio of the average kinetic energy of molecule A to that of molecule B is: 1:1 M A:M B M B:M A M A : M B What is the molar specific heat C V for a rigid non-linear triatomic gas? 3R 3 2 R 5 2 R 4R The value of = C P/C V for a gas with f degrees of freedom is 1 + 2/f . For a gas whose = 1.33 , the number of degrees of freedom is: 6 3 5 7 The degrees of freedom of a gas molecule depends on: The atomicity and structure of the molecule The pressure of the gas The volume of the container The number of moles of the gas