Page 1 For JEE Advanced Objective Questions Single Correct Option Q 1. The average velocity of molecules of a gas of molecular weight M at temperature T is (a) 3RT M (b) 8RT M ? (c) 2RT M (d) zero Q 2. Four particles have velocities 1,0,2 and 3 m/s. The root mean square velocity of the particles (definition wise) is (a) 3.5 m/s (b) 3.5 m / s (c) 1.5m/s (d) 14 m / s 3 Q 3. A steel rod of length 1 m is heated from 25° to 75°C keeping its length constant. The longitudinal strain developed in the rod is (Given coefficient of linear expansion of steel = 12 × 10 6 /°C) (a) 6 × 10 4 (b) 6 × 10 5 (c) 6 × 10 4 (d) zero Q 4. In a process the pressure of a gas remains constant. If the temperature is doubled, then the change in the volume will be (a) 100% (b) 200% (c) 50% (d) 25% Q 5. The average kinetic energy of the molecules of an ideal gas at 10°C has the value E. The temperature at which the kinetic energy of the same gas becomes 2E is (a) 5°C (b) 10°C (c) 40°C (d) None of these Q 6. A polyatomic gas with n degrees of freedom has a mean energy per molecule given by (a) n RT 2 (b) 1 RT 2 (c) n kT 2 (d) 1 kT 2 Q 7. The temperature of an ideal gas is increased from 27°C to 927°C. The rms speed of its molecules becomes (a) twice (b) half (c) four times (d) onefourth Q 8. In case of hydrogen and oxygen at NTP, which of the following is the same for both? (a) Average linear momentum per molecule (b) Average KE per molecule (c) KE per unit volume (d) KE per unit mass Q 9. Two thermally insulated vessels 1 and 2 are filled with air at temperatures (T1, T2 ), volumes (V1, V2) and pressures (P1, P2) respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be (P = common pressure) (a) T1 + T2 (b) (T1 +T2)/2 (c) 1 2 1 2 1 1 2 2 2 1 T T P(V V ) P V T P V T ? ? (d) 1 2 1 1 2 2 1 1 2 2 2 1 T T (P V P V ) P VT P V T ? ? Q 10. Two marks on a glass rod 10 cm apart are found to increase their distance by 0.08 mm when the rod is heated from 0°C to 100°C. A flask made of the same glass as that of rod measures a volume of 100 cc at 0°C. The volume it measures at 100°C in cc is (a) 100.24 (b) 100.12 (c) 100.36 (d) 100.48 Page 2 For JEE Advanced Objective Questions Single Correct Option Q 1. The average velocity of molecules of a gas of molecular weight M at temperature T is (a) 3RT M (b) 8RT M ? (c) 2RT M (d) zero Q 2. Four particles have velocities 1,0,2 and 3 m/s. The root mean square velocity of the particles (definition wise) is (a) 3.5 m/s (b) 3.5 m / s (c) 1.5m/s (d) 14 m / s 3 Q 3. A steel rod of length 1 m is heated from 25° to 75°C keeping its length constant. The longitudinal strain developed in the rod is (Given coefficient of linear expansion of steel = 12 × 10 6 /°C) (a) 6 × 10 4 (b) 6 × 10 5 (c) 6 × 10 4 (d) zero Q 4. In a process the pressure of a gas remains constant. If the temperature is doubled, then the change in the volume will be (a) 100% (b) 200% (c) 50% (d) 25% Q 5. The average kinetic energy of the molecules of an ideal gas at 10°C has the value E. The temperature at which the kinetic energy of the same gas becomes 2E is (a) 5°C (b) 10°C (c) 40°C (d) None of these Q 6. A polyatomic gas with n degrees of freedom has a mean energy per molecule given by (a) n RT 2 (b) 1 RT 2 (c) n kT 2 (d) 1 kT 2 Q 7. The temperature of an ideal gas is increased from 27°C to 927°C. The rms speed of its molecules becomes (a) twice (b) half (c) four times (d) onefourth Q 8. In case of hydrogen and oxygen at NTP, which of the following is the same for both? (a) Average linear momentum per molecule (b) Average KE per molecule (c) KE per unit volume (d) KE per unit mass Q 9. Two thermally insulated vessels 1 and 2 are filled with air at temperatures (T1, T2 ), volumes (V1, V2) and pressures (P1, P2) respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be (P = common pressure) (a) T1 + T2 (b) (T1 +T2)/2 (c) 1 2 1 2 1 1 2 2 2 1 T T P(V V ) P V T P V T ? ? (d) 1 2 1 1 2 2 1 1 2 2 2 1 T T (P V P V ) P VT P V T ? ? Q 10. Two marks on a glass rod 10 cm apart are found to increase their distance by 0.08 mm when the rod is heated from 0°C to 100°C. A flask made of the same glass as that of rod measures a volume of 100 cc at 0°C. The volume it measures at 100°C in cc is (a) 100.24 (b) 100.12 (c) 100.36 (d) 100.48 Q 11. The given curve represents the variation of temperature as a function of volume for one mole of an ideal gas. Which of the following curves best represents the variation of pressure as a function of volume? (a) (b) (c) (d) Q 12. A gas is found to obey the law P V = constant. The initial temperature and volume are T0 and V0. If the gas expands to a volume 3 V0, then the final temperature becomes (a) 0 3T (b) 0 2T (c) 0 T 3 (d) 0 T 2 Q 13. Air fills a room in winter at 7°C and in summer at 37°C. If the pressure is the same in winter and summer, the ratio of the weight of the air filled in winter and that in summer is (a) 2.2 (b) 1.75 (c) 1.1 (d) 3.3 Q 14. Three closed vessels A, B and C are at the same temperature T and contain gases which obey Maxwell distribution law of velocities. Vessels contains O2, B only N2 and C mixture of equal quantities of O2 and N2. If the average speed of the O2 molecules in vessel A is v 1 that of N2 molecules in vessel B is v2, then the average speed of the O2 molecules in vessel C is (a) 12 (v v ) 2 ? (b) v1 (c) 12 vv (d) None of these Q 15. In a very good vacuum system in the laboratory, the vacuum attained was 10 13 atm. If the temperature of the system was 300 K, the number of molecules present in a volume of 1 cm is (a) 2.4 × 10 6 (b) 24 (c) 2.4 × 10 9 (d) zero Q 16. If nitrogen gas molecule goes straight up with its rms speed at 0°C from the surface of the earth and there are no collisions with other molecules, then it will rise to an approximate height of (a) 8 km (b) 12 km (c) 12 m (d) 8 m Q 17. The coefficient of linear expansion of steel and brass are 11 × 10 6 /°C and 19 × 10 6 /°C respectively. If their difference in lengths at all temperatures has to kept constant at 30 cm, their lengths at 0°C should be (a) 71.25 cm and 41.25 cm (b) 82 cm and 52 cm (c) 92 cm and 62 cm (d) 62.25 cm and 32.25 cm Q 18. The given PU graph shows the variation of internal energy of an ideal gas with increase in pressure. Which of the following pressurevolume graph is equivalent to this graph? Page 3 For JEE Advanced Objective Questions Single Correct Option Q 1. The average velocity of molecules of a gas of molecular weight M at temperature T is (a) 3RT M (b) 8RT M ? (c) 2RT M (d) zero Q 2. Four particles have velocities 1,0,2 and 3 m/s. The root mean square velocity of the particles (definition wise) is (a) 3.5 m/s (b) 3.5 m / s (c) 1.5m/s (d) 14 m / s 3 Q 3. A steel rod of length 1 m is heated from 25° to 75°C keeping its length constant. The longitudinal strain developed in the rod is (Given coefficient of linear expansion of steel = 12 × 10 6 /°C) (a) 6 × 10 4 (b) 6 × 10 5 (c) 6 × 10 4 (d) zero Q 4. In a process the pressure of a gas remains constant. If the temperature is doubled, then the change in the volume will be (a) 100% (b) 200% (c) 50% (d) 25% Q 5. The average kinetic energy of the molecules of an ideal gas at 10°C has the value E. The temperature at which the kinetic energy of the same gas becomes 2E is (a) 5°C (b) 10°C (c) 40°C (d) None of these Q 6. A polyatomic gas with n degrees of freedom has a mean energy per molecule given by (a) n RT 2 (b) 1 RT 2 (c) n kT 2 (d) 1 kT 2 Q 7. The temperature of an ideal gas is increased from 27°C to 927°C. The rms speed of its molecules becomes (a) twice (b) half (c) four times (d) onefourth Q 8. In case of hydrogen and oxygen at NTP, which of the following is the same for both? (a) Average linear momentum per molecule (b) Average KE per molecule (c) KE per unit volume (d) KE per unit mass Q 9. Two thermally insulated vessels 1 and 2 are filled with air at temperatures (T1, T2 ), volumes (V1, V2) and pressures (P1, P2) respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be (P = common pressure) (a) T1 + T2 (b) (T1 +T2)/2 (c) 1 2 1 2 1 1 2 2 2 1 T T P(V V ) P V T P V T ? ? (d) 1 2 1 1 2 2 1 1 2 2 2 1 T T (P V P V ) P VT P V T ? ? Q 10. Two marks on a glass rod 10 cm apart are found to increase their distance by 0.08 mm when the rod is heated from 0°C to 100°C. A flask made of the same glass as that of rod measures a volume of 100 cc at 0°C. The volume it measures at 100°C in cc is (a) 100.24 (b) 100.12 (c) 100.36 (d) 100.48 Q 11. The given curve represents the variation of temperature as a function of volume for one mole of an ideal gas. Which of the following curves best represents the variation of pressure as a function of volume? (a) (b) (c) (d) Q 12. A gas is found to obey the law P V = constant. The initial temperature and volume are T0 and V0. If the gas expands to a volume 3 V0, then the final temperature becomes (a) 0 3T (b) 0 2T (c) 0 T 3 (d) 0 T 2 Q 13. Air fills a room in winter at 7°C and in summer at 37°C. If the pressure is the same in winter and summer, the ratio of the weight of the air filled in winter and that in summer is (a) 2.2 (b) 1.75 (c) 1.1 (d) 3.3 Q 14. Three closed vessels A, B and C are at the same temperature T and contain gases which obey Maxwell distribution law of velocities. Vessels contains O2, B only N2 and C mixture of equal quantities of O2 and N2. If the average speed of the O2 molecules in vessel A is v 1 that of N2 molecules in vessel B is v2, then the average speed of the O2 molecules in vessel C is (a) 12 (v v ) 2 ? (b) v1 (c) 12 vv (d) None of these Q 15. In a very good vacuum system in the laboratory, the vacuum attained was 10 13 atm. If the temperature of the system was 300 K, the number of molecules present in a volume of 1 cm is (a) 2.4 × 10 6 (b) 24 (c) 2.4 × 10 9 (d) zero Q 16. If nitrogen gas molecule goes straight up with its rms speed at 0°C from the surface of the earth and there are no collisions with other molecules, then it will rise to an approximate height of (a) 8 km (b) 12 km (c) 12 m (d) 8 m Q 17. The coefficient of linear expansion of steel and brass are 11 × 10 6 /°C and 19 × 10 6 /°C respectively. If their difference in lengths at all temperatures has to kept constant at 30 cm, their lengths at 0°C should be (a) 71.25 cm and 41.25 cm (b) 82 cm and 52 cm (c) 92 cm and 62 cm (d) 62.25 cm and 32.25 cm Q 18. The given PU graph shows the variation of internal energy of an ideal gas with increase in pressure. Which of the following pressurevolume graph is equivalent to this graph? (a) (b) (c) (d) Q 19. The expansion of an ideal gas of mass m at a constant pressure P is given by the straight line B. Then, the expansion of the same ideal gas of mass 2m at a pressure 2P is given by the straight line (a) C (b) A (c) B (d) data insufficient Q 20. 28 g of N2 gas is contained in a flask at a pressure of 10 atm and at a temperature of 57° C. It is round that due to leakage in the flask, the pressure is reduced to half and the temperature to 27°C. The quantity of N2 gas that leaked out is (a) 11/20 g (b) 20/11g (c) 5/63 g (d) 63/5 g Q 21. A mixture of 4g of hydrogen and 8 g of helium at NTP has a density about (a) 0.22 kg/m 3 (b) 0.62 kg/m 3 (c) 1.12 kg/m 3 (d) 0.13 kg/m 3 Q 22. The pressure (P) and the density ( ?) of given mass of a gas expressed by Boyle's law, P = K ? holds true (a) for any gas under any condition (b) for some gases under any conditions (c) only if the temperature is kept constant (d) None of these More than One Correct Options Q 23. During an experiment, an ideal gas is found to obey a condition 2 P ? = constant, ( ? = density of the gas). The gas is initially at temperature T, pressure P and density ?. The gas expands such that density changes to ?/2. (a) The pressure of the gas changes to 2P (b) The temperature of the gas changes to 2T (c) The graph of the above process on PT diagram is parabola (d) The graph of the above process on PT diagram is hyperbola Q 24. During an experiment, an ideal gas is found to obey a condition VP 2 = constant. The gas is initially at a temperature T, pressure P and volume V. The gas expands to volume 4V. Page 4 For JEE Advanced Objective Questions Single Correct Option Q 1. The average velocity of molecules of a gas of molecular weight M at temperature T is (a) 3RT M (b) 8RT M ? (c) 2RT M (d) zero Q 2. Four particles have velocities 1,0,2 and 3 m/s. The root mean square velocity of the particles (definition wise) is (a) 3.5 m/s (b) 3.5 m / s (c) 1.5m/s (d) 14 m / s 3 Q 3. A steel rod of length 1 m is heated from 25° to 75°C keeping its length constant. The longitudinal strain developed in the rod is (Given coefficient of linear expansion of steel = 12 × 10 6 /°C) (a) 6 × 10 4 (b) 6 × 10 5 (c) 6 × 10 4 (d) zero Q 4. In a process the pressure of a gas remains constant. If the temperature is doubled, then the change in the volume will be (a) 100% (b) 200% (c) 50% (d) 25% Q 5. The average kinetic energy of the molecules of an ideal gas at 10°C has the value E. The temperature at which the kinetic energy of the same gas becomes 2E is (a) 5°C (b) 10°C (c) 40°C (d) None of these Q 6. A polyatomic gas with n degrees of freedom has a mean energy per molecule given by (a) n RT 2 (b) 1 RT 2 (c) n kT 2 (d) 1 kT 2 Q 7. The temperature of an ideal gas is increased from 27°C to 927°C. The rms speed of its molecules becomes (a) twice (b) half (c) four times (d) onefourth Q 8. In case of hydrogen and oxygen at NTP, which of the following is the same for both? (a) Average linear momentum per molecule (b) Average KE per molecule (c) KE per unit volume (d) KE per unit mass Q 9. Two thermally insulated vessels 1 and 2 are filled with air at temperatures (T1, T2 ), volumes (V1, V2) and pressures (P1, P2) respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be (P = common pressure) (a) T1 + T2 (b) (T1 +T2)/2 (c) 1 2 1 2 1 1 2 2 2 1 T T P(V V ) P V T P V T ? ? (d) 1 2 1 1 2 2 1 1 2 2 2 1 T T (P V P V ) P VT P V T ? ? Q 10. Two marks on a glass rod 10 cm apart are found to increase their distance by 0.08 mm when the rod is heated from 0°C to 100°C. A flask made of the same glass as that of rod measures a volume of 100 cc at 0°C. The volume it measures at 100°C in cc is (a) 100.24 (b) 100.12 (c) 100.36 (d) 100.48 Q 11. The given curve represents the variation of temperature as a function of volume for one mole of an ideal gas. Which of the following curves best represents the variation of pressure as a function of volume? (a) (b) (c) (d) Q 12. A gas is found to obey the law P V = constant. The initial temperature and volume are T0 and V0. If the gas expands to a volume 3 V0, then the final temperature becomes (a) 0 3T (b) 0 2T (c) 0 T 3 (d) 0 T 2 Q 13. Air fills a room in winter at 7°C and in summer at 37°C. If the pressure is the same in winter and summer, the ratio of the weight of the air filled in winter and that in summer is (a) 2.2 (b) 1.75 (c) 1.1 (d) 3.3 Q 14. Three closed vessels A, B and C are at the same temperature T and contain gases which obey Maxwell distribution law of velocities. Vessels contains O2, B only N2 and C mixture of equal quantities of O2 and N2. If the average speed of the O2 molecules in vessel A is v 1 that of N2 molecules in vessel B is v2, then the average speed of the O2 molecules in vessel C is (a) 12 (v v ) 2 ? (b) v1 (c) 12 vv (d) None of these Q 15. In a very good vacuum system in the laboratory, the vacuum attained was 10 13 atm. If the temperature of the system was 300 K, the number of molecules present in a volume of 1 cm is (a) 2.4 × 10 6 (b) 24 (c) 2.4 × 10 9 (d) zero Q 16. If nitrogen gas molecule goes straight up with its rms speed at 0°C from the surface of the earth and there are no collisions with other molecules, then it will rise to an approximate height of (a) 8 km (b) 12 km (c) 12 m (d) 8 m Q 17. The coefficient of linear expansion of steel and brass are 11 × 10 6 /°C and 19 × 10 6 /°C respectively. If their difference in lengths at all temperatures has to kept constant at 30 cm, their lengths at 0°C should be (a) 71.25 cm and 41.25 cm (b) 82 cm and 52 cm (c) 92 cm and 62 cm (d) 62.25 cm and 32.25 cm Q 18. The given PU graph shows the variation of internal energy of an ideal gas with increase in pressure. Which of the following pressurevolume graph is equivalent to this graph? (a) (b) (c) (d) Q 19. The expansion of an ideal gas of mass m at a constant pressure P is given by the straight line B. Then, the expansion of the same ideal gas of mass 2m at a pressure 2P is given by the straight line (a) C (b) A (c) B (d) data insufficient Q 20. 28 g of N2 gas is contained in a flask at a pressure of 10 atm and at a temperature of 57° C. It is round that due to leakage in the flask, the pressure is reduced to half and the temperature to 27°C. The quantity of N2 gas that leaked out is (a) 11/20 g (b) 20/11g (c) 5/63 g (d) 63/5 g Q 21. A mixture of 4g of hydrogen and 8 g of helium at NTP has a density about (a) 0.22 kg/m 3 (b) 0.62 kg/m 3 (c) 1.12 kg/m 3 (d) 0.13 kg/m 3 Q 22. The pressure (P) and the density ( ?) of given mass of a gas expressed by Boyle's law, P = K ? holds true (a) for any gas under any condition (b) for some gases under any conditions (c) only if the temperature is kept constant (d) None of these More than One Correct Options Q 23. During an experiment, an ideal gas is found to obey a condition 2 P ? = constant, ( ? = density of the gas). The gas is initially at temperature T, pressure P and density ?. The gas expands such that density changes to ?/2. (a) The pressure of the gas changes to 2P (b) The temperature of the gas changes to 2T (c) The graph of the above process on PT diagram is parabola (d) The graph of the above process on PT diagram is hyperbola Q 24. During an experiment, an ideal gas is found to obey a condition VP 2 = constant. The gas is initially at a temperature T, pressure P and volume V. The gas expands to volume 4V. (a) The pressure of gas changes to P 2 (b) The temperature of gas changes to 4T (c) The graph of the above process on PT diagram is parabola (d) The graph of the above process on PT diagram is hyperbola Q 25. Find the correct options (a) Ice point in Fahrenheit scale is 32°F (b) Ice point in Fahrenheit scale is 98.8°F (c) Steam point in Fahrenheit scale is 212°F (d) Steam point in Fahrenheit scale is 252°F Q 26. In the P F diagram shown in figure, choose the correct options for the process ab : (a) density of gas has reduced to half (b) temperature of gas has increased to two times (c) internal energy of gas has increased to four times (d) TV graph is a parabola passing through origin Q 27. Choose the wrong options (a) Translational kinetic energy of all ideal gases at same temperature is same (b) In one degree of freedom all ideal gases has internal energy 1 RT 2 ? (c) Translational degree of freedom of all ideal gases is three (d) Translational kinetic energy of one mole of all ideal gases is 3 RT 2 Q 28. Along the line1, mass of gas is m l and pressure is P1. Along the line2 mass of same gas is m 2 and pressure is P2. Choose the correct options. (a) m 1 may be less than m 2 (b) m 2 may be less than m 1 (c) P1 may be less than P2 (d) P2 may be less than P1 Q 29. Choose the correct options (a) In m P RT M ? , m is mass of gas per unit volume (b) In m PV RT M ? , m is mass of one molecule of gas (c) In 2 rms 1 mN Pv 3V ? , m is total mass of gas. Page 5 For JEE Advanced Objective Questions Single Correct Option Q 1. The average velocity of molecules of a gas of molecular weight M at temperature T is (a) 3RT M (b) 8RT M ? (c) 2RT M (d) zero Q 2. Four particles have velocities 1,0,2 and 3 m/s. The root mean square velocity of the particles (definition wise) is (a) 3.5 m/s (b) 3.5 m / s (c) 1.5m/s (d) 14 m / s 3 Q 3. A steel rod of length 1 m is heated from 25° to 75°C keeping its length constant. The longitudinal strain developed in the rod is (Given coefficient of linear expansion of steel = 12 × 10 6 /°C) (a) 6 × 10 4 (b) 6 × 10 5 (c) 6 × 10 4 (d) zero Q 4. In a process the pressure of a gas remains constant. If the temperature is doubled, then the change in the volume will be (a) 100% (b) 200% (c) 50% (d) 25% Q 5. The average kinetic energy of the molecules of an ideal gas at 10°C has the value E. The temperature at which the kinetic energy of the same gas becomes 2E is (a) 5°C (b) 10°C (c) 40°C (d) None of these Q 6. A polyatomic gas with n degrees of freedom has a mean energy per molecule given by (a) n RT 2 (b) 1 RT 2 (c) n kT 2 (d) 1 kT 2 Q 7. The temperature of an ideal gas is increased from 27°C to 927°C. The rms speed of its molecules becomes (a) twice (b) half (c) four times (d) onefourth Q 8. In case of hydrogen and oxygen at NTP, which of the following is the same for both? (a) Average linear momentum per molecule (b) Average KE per molecule (c) KE per unit volume (d) KE per unit mass Q 9. Two thermally insulated vessels 1 and 2 are filled with air at temperatures (T1, T2 ), volumes (V1, V2) and pressures (P1, P2) respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be (P = common pressure) (a) T1 + T2 (b) (T1 +T2)/2 (c) 1 2 1 2 1 1 2 2 2 1 T T P(V V ) P V T P V T ? ? (d) 1 2 1 1 2 2 1 1 2 2 2 1 T T (P V P V ) P VT P V T ? ? Q 10. Two marks on a glass rod 10 cm apart are found to increase their distance by 0.08 mm when the rod is heated from 0°C to 100°C. A flask made of the same glass as that of rod measures a volume of 100 cc at 0°C. The volume it measures at 100°C in cc is (a) 100.24 (b) 100.12 (c) 100.36 (d) 100.48 Q 11. The given curve represents the variation of temperature as a function of volume for one mole of an ideal gas. Which of the following curves best represents the variation of pressure as a function of volume? (a) (b) (c) (d) Q 12. A gas is found to obey the law P V = constant. The initial temperature and volume are T0 and V0. If the gas expands to a volume 3 V0, then the final temperature becomes (a) 0 3T (b) 0 2T (c) 0 T 3 (d) 0 T 2 Q 13. Air fills a room in winter at 7°C and in summer at 37°C. If the pressure is the same in winter and summer, the ratio of the weight of the air filled in winter and that in summer is (a) 2.2 (b) 1.75 (c) 1.1 (d) 3.3 Q 14. Three closed vessels A, B and C are at the same temperature T and contain gases which obey Maxwell distribution law of velocities. Vessels contains O2, B only N2 and C mixture of equal quantities of O2 and N2. If the average speed of the O2 molecules in vessel A is v 1 that of N2 molecules in vessel B is v2, then the average speed of the O2 molecules in vessel C is (a) 12 (v v ) 2 ? (b) v1 (c) 12 vv (d) None of these Q 15. In a very good vacuum system in the laboratory, the vacuum attained was 10 13 atm. If the temperature of the system was 300 K, the number of molecules present in a volume of 1 cm is (a) 2.4 × 10 6 (b) 24 (c) 2.4 × 10 9 (d) zero Q 16. If nitrogen gas molecule goes straight up with its rms speed at 0°C from the surface of the earth and there are no collisions with other molecules, then it will rise to an approximate height of (a) 8 km (b) 12 km (c) 12 m (d) 8 m Q 17. The coefficient of linear expansion of steel and brass are 11 × 10 6 /°C and 19 × 10 6 /°C respectively. If their difference in lengths at all temperatures has to kept constant at 30 cm, their lengths at 0°C should be (a) 71.25 cm and 41.25 cm (b) 82 cm and 52 cm (c) 92 cm and 62 cm (d) 62.25 cm and 32.25 cm Q 18. The given PU graph shows the variation of internal energy of an ideal gas with increase in pressure. Which of the following pressurevolume graph is equivalent to this graph? (a) (b) (c) (d) Q 19. The expansion of an ideal gas of mass m at a constant pressure P is given by the straight line B. Then, the expansion of the same ideal gas of mass 2m at a pressure 2P is given by the straight line (a) C (b) A (c) B (d) data insufficient Q 20. 28 g of N2 gas is contained in a flask at a pressure of 10 atm and at a temperature of 57° C. It is round that due to leakage in the flask, the pressure is reduced to half and the temperature to 27°C. The quantity of N2 gas that leaked out is (a) 11/20 g (b) 20/11g (c) 5/63 g (d) 63/5 g Q 21. A mixture of 4g of hydrogen and 8 g of helium at NTP has a density about (a) 0.22 kg/m 3 (b) 0.62 kg/m 3 (c) 1.12 kg/m 3 (d) 0.13 kg/m 3 Q 22. The pressure (P) and the density ( ?) of given mass of a gas expressed by Boyle's law, P = K ? holds true (a) for any gas under any condition (b) for some gases under any conditions (c) only if the temperature is kept constant (d) None of these More than One Correct Options Q 23. During an experiment, an ideal gas is found to obey a condition 2 P ? = constant, ( ? = density of the gas). The gas is initially at temperature T, pressure P and density ?. The gas expands such that density changes to ?/2. (a) The pressure of the gas changes to 2P (b) The temperature of the gas changes to 2T (c) The graph of the above process on PT diagram is parabola (d) The graph of the above process on PT diagram is hyperbola Q 24. During an experiment, an ideal gas is found to obey a condition VP 2 = constant. The gas is initially at a temperature T, pressure P and volume V. The gas expands to volume 4V. (a) The pressure of gas changes to P 2 (b) The temperature of gas changes to 4T (c) The graph of the above process on PT diagram is parabola (d) The graph of the above process on PT diagram is hyperbola Q 25. Find the correct options (a) Ice point in Fahrenheit scale is 32°F (b) Ice point in Fahrenheit scale is 98.8°F (c) Steam point in Fahrenheit scale is 212°F (d) Steam point in Fahrenheit scale is 252°F Q 26. In the P F diagram shown in figure, choose the correct options for the process ab : (a) density of gas has reduced to half (b) temperature of gas has increased to two times (c) internal energy of gas has increased to four times (d) TV graph is a parabola passing through origin Q 27. Choose the wrong options (a) Translational kinetic energy of all ideal gases at same temperature is same (b) In one degree of freedom all ideal gases has internal energy 1 RT 2 ? (c) Translational degree of freedom of all ideal gases is three (d) Translational kinetic energy of one mole of all ideal gases is 3 RT 2 Q 28. Along the line1, mass of gas is m l and pressure is P1. Along the line2 mass of same gas is m 2 and pressure is P2. Choose the correct options. (a) m 1 may be less than m 2 (b) m 2 may be less than m 1 (c) P1 may be less than P2 (d) P2 may be less than P1 Q 29. Choose the correct options (a) In m P RT M ? , m is mass of gas per unit volume (b) In m PV RT M ? , m is mass of one molecule of gas (c) In 2 rms 1 mN Pv 3V ? , m is total mass of gas. (d) In rms 3kT v m ? , m is mass of one molecule of gas Answers 1.(b) 2.(b) 3.(c) 4.(a) 5.(d) 6.(c) 7.(a) 8.(b) 9.(c) 10, (a) 11.(a) 12. (a) 13.(c) 14. (b) 15.(a) 16. (b) 17. (a) 18.(b) 19. (c) 20. (d) 21.(d) 22.(c) More than One Correct Options 23. (b,d) 24. (a,d) 25. (a,c) 26. (a,c,d) 27. (a,b) 28. (a,b,c,d) 29. (a,d) Solutions 1. No required. 2. 3. It means rod is compressed from its natural length by ?l = 6 × 10 4 4. If P = constant, then V ? T 5. E ? T ? T2 = 2T1 = 2 (273+ 10)= 566 K = 293°C 6. Not required. 7. T1 = 273 + 27 = 300 K T2 = 273+ 927 = 1200K v rms ? T T has becomes four times. Therefore vrms will become two times. 8. Hydrogen and oxygen both are diatomic gases. Therefore, average kinetic energy per molecule is (as f = 5) 9. (n1 + n2)i = (n1 + n 2)f Solving we get, 10. ?l = l ? ? ? = 0.24 ccRead More
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