Page 1 Exercises For JEE Main Subjective Questions Temperature Scales Q 1. Change each of the given temperatures to the Celsius and Kelvin scales: 68° F, 5° F and 176° F. Q 2. Change each of the given temperatures to the Fahrenheit and Rankine scales: 30° C, 5° C and 20° C. Q 3. At what temperature do the Celsius and Fahrenheit readings have the same numerical value? Q 4. You work in a materials testing lab and your boss tells you to increase the temperature of a sample by 40.0° C The only thermometer you can find at your workbench reads in ° F. If the initial temperature of the sample is 68.2° F. What is its temperature in ° F, when the desired temperature increase has been achieved? Q 5. The steam point and the ice point of a mercury thermometer are marked as 80° and 20°. What will be the temperature in centigrade mercury scale when this thermometer reads 32° ? Thermometers Q 6. The pressure of the gas in a constant volume gas thermometer is 80cm of mercury in melting ice. When the bulb is placed in a liquid, the pressure becomes 160 cm of mercury. Find the temperature of the liquid. Q 7. The resistances of a platinum resistance thermometer at the ice point, the steam point and the boiling point of sulphur are 2.50, 3.50and 6.50 ? respectively. Find the boiling point of sulphur on the platinum scale. The ice point and the steam point measure 0° and 100° respectively. Q 8. In a constant volume gas thermometer, the pressure of the working gas is measured by the difference in the levels of mercury in the two arms of a Utube connected to the gas at one end . When the bulb is placed at the room temperature 27.0° C, the mercury column in the arm open to atmosphere stands 5.00cm above the level of mercury in the other arm. When the bulb is placed in a hot liquid, the difference of mercury levels becomes 45.0cm. Calculate the temperature of the liquid.(Atmospheric pressure = 75.0cm of mercury.) Thermal Expansion (Take values of a from table 17.1) Q 9. An iron ball has a diameter of 6 cm and is 0.010 mm too large to pass through a hole in a brass plate when the ball and plate are at a temperature of 30° C At what temperature, the same for ball and plate, will the ball just pass through the hole ? Q 10. (a) An aluminum measuring rod which is correct at 5° C, measures a certain distance as 88.42cm at 35 ° C. Determine the error in measuring the distance due to the expansion of the rod. (b) If this aluminum rod measures a length of steel as 88.42 cm at 35° C, what is the correct length of the steel at 35° C? Q 11. A steel tape is calibrated at 20° C. On a cold day when the temperature is 15° C, what will be the percentage error in the tape ? Page 2 Exercises For JEE Main Subjective Questions Temperature Scales Q 1. Change each of the given temperatures to the Celsius and Kelvin scales: 68° F, 5° F and 176° F. Q 2. Change each of the given temperatures to the Fahrenheit and Rankine scales: 30° C, 5° C and 20° C. Q 3. At what temperature do the Celsius and Fahrenheit readings have the same numerical value? Q 4. You work in a materials testing lab and your boss tells you to increase the temperature of a sample by 40.0° C The only thermometer you can find at your workbench reads in ° F. If the initial temperature of the sample is 68.2° F. What is its temperature in ° F, when the desired temperature increase has been achieved? Q 5. The steam point and the ice point of a mercury thermometer are marked as 80° and 20°. What will be the temperature in centigrade mercury scale when this thermometer reads 32° ? Thermometers Q 6. The pressure of the gas in a constant volume gas thermometer is 80cm of mercury in melting ice. When the bulb is placed in a liquid, the pressure becomes 160 cm of mercury. Find the temperature of the liquid. Q 7. The resistances of a platinum resistance thermometer at the ice point, the steam point and the boiling point of sulphur are 2.50, 3.50and 6.50 ? respectively. Find the boiling point of sulphur on the platinum scale. The ice point and the steam point measure 0° and 100° respectively. Q 8. In a constant volume gas thermometer, the pressure of the working gas is measured by the difference in the levels of mercury in the two arms of a Utube connected to the gas at one end . When the bulb is placed at the room temperature 27.0° C, the mercury column in the arm open to atmosphere stands 5.00cm above the level of mercury in the other arm. When the bulb is placed in a hot liquid, the difference of mercury levels becomes 45.0cm. Calculate the temperature of the liquid.(Atmospheric pressure = 75.0cm of mercury.) Thermal Expansion (Take values of a from table 17.1) Q 9. An iron ball has a diameter of 6 cm and is 0.010 mm too large to pass through a hole in a brass plate when the ball and plate are at a temperature of 30° C At what temperature, the same for ball and plate, will the ball just pass through the hole ? Q 10. (a) An aluminum measuring rod which is correct at 5° C, measures a certain distance as 88.42cm at 35 ° C. Determine the error in measuring the distance due to the expansion of the rod. (b) If this aluminum rod measures a length of steel as 88.42 cm at 35° C, what is the correct length of the steel at 35° C? Q 11. A steel tape is calibrated at 20° C. On a cold day when the temperature is 15° C, what will be the percentage error in the tape ? Q 12. A steel wire of 2.0 mm 2 crosssection is held straight (but under no tension) by attaching it firmly to two points a distance 1.50mapart at 30 ° C. If the temperature now decreases to 10° C and if the two points remain fixed, what will be the tension in the wire ? For steel, Y = 20,0000 MP a. Q 13. A metallic bob weighs 50 g in air. If it is immersed in a liquid at a temperature of 25° C, it weighs 45 g. When the temperature of the liquid is raised to 100° C, it weighs 45. lg. Calculate the coefficient of cubical expansion of the liquid. Given that coefficient of cubical expansion of the metal is 12 × 10 6 ° C 1 . Gas Laws and ideal Gas Equation Q 14. Find the mass (in kilogram) of an ammonia molecule NH 3. Q 15. An ideal gas exerts a pressure of 1.52 MPa when its temperature is 298.15 K and its volume is 10 2 m 3 . (a) How many moles of gas are there? (b) What is the mass density if the gas is molecular hydrogen? (c) What is the mass density if the gas is oxygen? Q 16. A compressor pumps 70 L of air into a 6 L tank with the temperature remaining unchanged. If all the air is originally at 1 atm. What is the final absolute pressure of the air in the tank? Q 17. A partially inflated balloon contains 500 m 3 of helium at 27° C and 1 atm pressure. What is the volume of the helium at an altitude of 18000 ft, where the pressure is 0.5 atm and the temperature is 3° C? Q 18. A cylinder whose inside diameter is 4.00 cm contains air compressed by a piston of mass m= 13.0 kg which can slide freely in the cylinder. The entire arrangement is immersed in a water bath whose temperature can be controlled. The system is initially in equilibrium at temperature t i =20°C. The initial height of the piston above the bottom of the cylinder is hi = 4.00cm The temperature of the water bath is gradually increased to a final temperature t f = 100° C. Calculate the final height hf of the piston. Q 19. The closed cylinder shown in figure has a freely moving piston separating chambers 1 and 2. Chamber 1 contains 25 mg of N2 gas and chamber 2 contains 40 mg of helium gas. When equilibrium is established what will be the ratio L1 /L2 ? What is the ratio of the number of moles of N2 to the number of moles of He? (Molecular weights of N 2 and He are 28 and 4). Page 3 Exercises For JEE Main Subjective Questions Temperature Scales Q 1. Change each of the given temperatures to the Celsius and Kelvin scales: 68° F, 5° F and 176° F. Q 2. Change each of the given temperatures to the Fahrenheit and Rankine scales: 30° C, 5° C and 20° C. Q 3. At what temperature do the Celsius and Fahrenheit readings have the same numerical value? Q 4. You work in a materials testing lab and your boss tells you to increase the temperature of a sample by 40.0° C The only thermometer you can find at your workbench reads in ° F. If the initial temperature of the sample is 68.2° F. What is its temperature in ° F, when the desired temperature increase has been achieved? Q 5. The steam point and the ice point of a mercury thermometer are marked as 80° and 20°. What will be the temperature in centigrade mercury scale when this thermometer reads 32° ? Thermometers Q 6. The pressure of the gas in a constant volume gas thermometer is 80cm of mercury in melting ice. When the bulb is placed in a liquid, the pressure becomes 160 cm of mercury. Find the temperature of the liquid. Q 7. The resistances of a platinum resistance thermometer at the ice point, the steam point and the boiling point of sulphur are 2.50, 3.50and 6.50 ? respectively. Find the boiling point of sulphur on the platinum scale. The ice point and the steam point measure 0° and 100° respectively. Q 8. In a constant volume gas thermometer, the pressure of the working gas is measured by the difference in the levels of mercury in the two arms of a Utube connected to the gas at one end . When the bulb is placed at the room temperature 27.0° C, the mercury column in the arm open to atmosphere stands 5.00cm above the level of mercury in the other arm. When the bulb is placed in a hot liquid, the difference of mercury levels becomes 45.0cm. Calculate the temperature of the liquid.(Atmospheric pressure = 75.0cm of mercury.) Thermal Expansion (Take values of a from table 17.1) Q 9. An iron ball has a diameter of 6 cm and is 0.010 mm too large to pass through a hole in a brass plate when the ball and plate are at a temperature of 30° C At what temperature, the same for ball and plate, will the ball just pass through the hole ? Q 10. (a) An aluminum measuring rod which is correct at 5° C, measures a certain distance as 88.42cm at 35 ° C. Determine the error in measuring the distance due to the expansion of the rod. (b) If this aluminum rod measures a length of steel as 88.42 cm at 35° C, what is the correct length of the steel at 35° C? Q 11. A steel tape is calibrated at 20° C. On a cold day when the temperature is 15° C, what will be the percentage error in the tape ? Q 12. A steel wire of 2.0 mm 2 crosssection is held straight (but under no tension) by attaching it firmly to two points a distance 1.50mapart at 30 ° C. If the temperature now decreases to 10° C and if the two points remain fixed, what will be the tension in the wire ? For steel, Y = 20,0000 MP a. Q 13. A metallic bob weighs 50 g in air. If it is immersed in a liquid at a temperature of 25° C, it weighs 45 g. When the temperature of the liquid is raised to 100° C, it weighs 45. lg. Calculate the coefficient of cubical expansion of the liquid. Given that coefficient of cubical expansion of the metal is 12 × 10 6 ° C 1 . Gas Laws and ideal Gas Equation Q 14. Find the mass (in kilogram) of an ammonia molecule NH 3. Q 15. An ideal gas exerts a pressure of 1.52 MPa when its temperature is 298.15 K and its volume is 10 2 m 3 . (a) How many moles of gas are there? (b) What is the mass density if the gas is molecular hydrogen? (c) What is the mass density if the gas is oxygen? Q 16. A compressor pumps 70 L of air into a 6 L tank with the temperature remaining unchanged. If all the air is originally at 1 atm. What is the final absolute pressure of the air in the tank? Q 17. A partially inflated balloon contains 500 m 3 of helium at 27° C and 1 atm pressure. What is the volume of the helium at an altitude of 18000 ft, where the pressure is 0.5 atm and the temperature is 3° C? Q 18. A cylinder whose inside diameter is 4.00 cm contains air compressed by a piston of mass m= 13.0 kg which can slide freely in the cylinder. The entire arrangement is immersed in a water bath whose temperature can be controlled. The system is initially in equilibrium at temperature t i =20°C. The initial height of the piston above the bottom of the cylinder is hi = 4.00cm The temperature of the water bath is gradually increased to a final temperature t f = 100° C. Calculate the final height hf of the piston. Q 19. The closed cylinder shown in figure has a freely moving piston separating chambers 1 and 2. Chamber 1 contains 25 mg of N2 gas and chamber 2 contains 40 mg of helium gas. When equilibrium is established what will be the ratio L1 /L2 ? What is the ratio of the number of moles of N2 to the number of moles of He? (Molecular weights of N 2 and He are 28 and 4). Q 20. Two gases occupy two containers A and B. The gas in A of volume 0.11m 3 exerts a pressure of 1.38 MPa. The gas in B of volume 0.16 m 3 exerts a pressure of 0.69 MPa. Two containers are united by a tube of negligible volume and the gases are allowed to intermingle. What is the final pressure in the container if the temperature remains constant ? Q 21. A glass bulb of volume 400cm 3 is connected to another of volume 200cm 3 by means of a tube of negligible volume. The bulbs contain dry air and are both at a common temperature and pressure of 20°C and 1.00 atm. The larger bulb is immersed in steam at 100°C and the smaller in melting ice at 0°C. Find the final common pressure. Q 22. The condition called standard temperature and pressure (STP) for a gas is defined as temperature of 0°C = 273.15K and a pressure of 1 atm = 1.013 × 10 5 Pa. If you want to keep a mole of an ideal gas in your room at STP, how big a container do you need? Q 23. A large cylindrical tank contains 0.750 m 3 of nitrogen gas at 27° C and 1.50 × 10 5 Pa (absolute pressure). The tank has a tightfitting piston that allows the volume to be changed. What will be the pressure if the volume is decreased to 0.480 m 3 and the temperature is increased to 157°C. Q 24. A vessel of volume 5 litres contains 1.4 g of N2 and 0.4 g of He at 1500 K. If 30% of the nitrogen molecules are dissociated into atoms then find the gas pressure. Degree of Freedom, internal Energy and Molar Heat Capacity Q 25. Temperature of diatomic gas is 300 K. If moment of inertia of its molecules is 8.28 × 10 38 gcm 2 . Calculate their root mean square angular velocity. Q 26. How many degrees of freedom have the gas molecules, if under standard conditions the gas density is ? = 1.3 kg/m 3 and velocity of sound propagation on it is v = 330 m/s? Q 27. Three moles of an ideal gas having ? = 1.67 are mixed with 2 moles of another ideal gas having y = 1.4. Find the equivalent value of ? for the mixture. Q 28. If the kinetic energy of the molecules in 5 litres of helium at 2 atm is E. What is the kinetic energy of molecules in 15 litres of oxygen at 3 atm in terms of E ? Q 29. Find the number of degrees of freedom of molecules in a gas. Whose molar heat capacity (a) at constant pressure CP = 29 J mol 1 K 1 (b) C = 29 J mol 1 K 1 in the process PT = constant. Q 30. In a certain gas 2 th 5 of the energy of molecules is associated with the rotation of molecules and the rest of it is associated with the motion of the centre of mass. (a) What is the average translational energy of one such molecule when the temperature is 27°C? (b) How much energy must be supplied to one mole of this gas at constant volume to raise the temperature by 1 °C? Q 31. A mixture contains 1 mole of helium (CP =2.5R, CV =1.5R) and 1 mole of hydrogen (CP =3.5R,CV = 2.5 R). Calculate the values of CP,CV and ? for the mixture. Q 32. Two ideal gases have the same value of C P / CV = ?. What will be the value of this ratio for a mixture of the two such gases in the ratio 1 : 2 ? Page 4 Exercises For JEE Main Subjective Questions Temperature Scales Q 1. Change each of the given temperatures to the Celsius and Kelvin scales: 68° F, 5° F and 176° F. Q 2. Change each of the given temperatures to the Fahrenheit and Rankine scales: 30° C, 5° C and 20° C. Q 3. At what temperature do the Celsius and Fahrenheit readings have the same numerical value? Q 4. You work in a materials testing lab and your boss tells you to increase the temperature of a sample by 40.0° C The only thermometer you can find at your workbench reads in ° F. If the initial temperature of the sample is 68.2° F. What is its temperature in ° F, when the desired temperature increase has been achieved? Q 5. The steam point and the ice point of a mercury thermometer are marked as 80° and 20°. What will be the temperature in centigrade mercury scale when this thermometer reads 32° ? Thermometers Q 6. The pressure of the gas in a constant volume gas thermometer is 80cm of mercury in melting ice. When the bulb is placed in a liquid, the pressure becomes 160 cm of mercury. Find the temperature of the liquid. Q 7. The resistances of a platinum resistance thermometer at the ice point, the steam point and the boiling point of sulphur are 2.50, 3.50and 6.50 ? respectively. Find the boiling point of sulphur on the platinum scale. The ice point and the steam point measure 0° and 100° respectively. Q 8. In a constant volume gas thermometer, the pressure of the working gas is measured by the difference in the levels of mercury in the two arms of a Utube connected to the gas at one end . When the bulb is placed at the room temperature 27.0° C, the mercury column in the arm open to atmosphere stands 5.00cm above the level of mercury in the other arm. When the bulb is placed in a hot liquid, the difference of mercury levels becomes 45.0cm. Calculate the temperature of the liquid.(Atmospheric pressure = 75.0cm of mercury.) Thermal Expansion (Take values of a from table 17.1) Q 9. An iron ball has a diameter of 6 cm and is 0.010 mm too large to pass through a hole in a brass plate when the ball and plate are at a temperature of 30° C At what temperature, the same for ball and plate, will the ball just pass through the hole ? Q 10. (a) An aluminum measuring rod which is correct at 5° C, measures a certain distance as 88.42cm at 35 ° C. Determine the error in measuring the distance due to the expansion of the rod. (b) If this aluminum rod measures a length of steel as 88.42 cm at 35° C, what is the correct length of the steel at 35° C? Q 11. A steel tape is calibrated at 20° C. On a cold day when the temperature is 15° C, what will be the percentage error in the tape ? Q 12. A steel wire of 2.0 mm 2 crosssection is held straight (but under no tension) by attaching it firmly to two points a distance 1.50mapart at 30 ° C. If the temperature now decreases to 10° C and if the two points remain fixed, what will be the tension in the wire ? For steel, Y = 20,0000 MP a. Q 13. A metallic bob weighs 50 g in air. If it is immersed in a liquid at a temperature of 25° C, it weighs 45 g. When the temperature of the liquid is raised to 100° C, it weighs 45. lg. Calculate the coefficient of cubical expansion of the liquid. Given that coefficient of cubical expansion of the metal is 12 × 10 6 ° C 1 . Gas Laws and ideal Gas Equation Q 14. Find the mass (in kilogram) of an ammonia molecule NH 3. Q 15. An ideal gas exerts a pressure of 1.52 MPa when its temperature is 298.15 K and its volume is 10 2 m 3 . (a) How many moles of gas are there? (b) What is the mass density if the gas is molecular hydrogen? (c) What is the mass density if the gas is oxygen? Q 16. A compressor pumps 70 L of air into a 6 L tank with the temperature remaining unchanged. If all the air is originally at 1 atm. What is the final absolute pressure of the air in the tank? Q 17. A partially inflated balloon contains 500 m 3 of helium at 27° C and 1 atm pressure. What is the volume of the helium at an altitude of 18000 ft, where the pressure is 0.5 atm and the temperature is 3° C? Q 18. A cylinder whose inside diameter is 4.00 cm contains air compressed by a piston of mass m= 13.0 kg which can slide freely in the cylinder. The entire arrangement is immersed in a water bath whose temperature can be controlled. The system is initially in equilibrium at temperature t i =20°C. The initial height of the piston above the bottom of the cylinder is hi = 4.00cm The temperature of the water bath is gradually increased to a final temperature t f = 100° C. Calculate the final height hf of the piston. Q 19. The closed cylinder shown in figure has a freely moving piston separating chambers 1 and 2. Chamber 1 contains 25 mg of N2 gas and chamber 2 contains 40 mg of helium gas. When equilibrium is established what will be the ratio L1 /L2 ? What is the ratio of the number of moles of N2 to the number of moles of He? (Molecular weights of N 2 and He are 28 and 4). Q 20. Two gases occupy two containers A and B. The gas in A of volume 0.11m 3 exerts a pressure of 1.38 MPa. The gas in B of volume 0.16 m 3 exerts a pressure of 0.69 MPa. Two containers are united by a tube of negligible volume and the gases are allowed to intermingle. What is the final pressure in the container if the temperature remains constant ? Q 21. A glass bulb of volume 400cm 3 is connected to another of volume 200cm 3 by means of a tube of negligible volume. The bulbs contain dry air and are both at a common temperature and pressure of 20°C and 1.00 atm. The larger bulb is immersed in steam at 100°C and the smaller in melting ice at 0°C. Find the final common pressure. Q 22. The condition called standard temperature and pressure (STP) for a gas is defined as temperature of 0°C = 273.15K and a pressure of 1 atm = 1.013 × 10 5 Pa. If you want to keep a mole of an ideal gas in your room at STP, how big a container do you need? Q 23. A large cylindrical tank contains 0.750 m 3 of nitrogen gas at 27° C and 1.50 × 10 5 Pa (absolute pressure). The tank has a tightfitting piston that allows the volume to be changed. What will be the pressure if the volume is decreased to 0.480 m 3 and the temperature is increased to 157°C. Q 24. A vessel of volume 5 litres contains 1.4 g of N2 and 0.4 g of He at 1500 K. If 30% of the nitrogen molecules are dissociated into atoms then find the gas pressure. Degree of Freedom, internal Energy and Molar Heat Capacity Q 25. Temperature of diatomic gas is 300 K. If moment of inertia of its molecules is 8.28 × 10 38 gcm 2 . Calculate their root mean square angular velocity. Q 26. How many degrees of freedom have the gas molecules, if under standard conditions the gas density is ? = 1.3 kg/m 3 and velocity of sound propagation on it is v = 330 m/s? Q 27. Three moles of an ideal gas having ? = 1.67 are mixed with 2 moles of another ideal gas having y = 1.4. Find the equivalent value of ? for the mixture. Q 28. If the kinetic energy of the molecules in 5 litres of helium at 2 atm is E. What is the kinetic energy of molecules in 15 litres of oxygen at 3 atm in terms of E ? Q 29. Find the number of degrees of freedom of molecules in a gas. Whose molar heat capacity (a) at constant pressure CP = 29 J mol 1 K 1 (b) C = 29 J mol 1 K 1 in the process PT = constant. Q 30. In a certain gas 2 th 5 of the energy of molecules is associated with the rotation of molecules and the rest of it is associated with the motion of the centre of mass. (a) What is the average translational energy of one such molecule when the temperature is 27°C? (b) How much energy must be supplied to one mole of this gas at constant volume to raise the temperature by 1 °C? Q 31. A mixture contains 1 mole of helium (CP =2.5R, CV =1.5R) and 1 mole of hydrogen (CP =3.5R,CV = 2.5 R). Calculate the values of CP,CV and ? for the mixture. Q 32. Two ideal gases have the same value of C P / CV = ?. What will be the value of this ratio for a mixture of the two such gases in the ratio 1 : 2 ? Q 33. An ideal gas (CP / CV = ?) is taken through a process in which the pressure and the volume vary as P = aV b . Find the value of b for which the specific heat capacity in the process is zero. Q 34. An ideal gas is taken through a process in which the pressure and the volume are changed according to the equation P = kV. Show that the molar heat capacity of the gas for the process is given by C = CV + R 2 Kinetic Theory of Gases Q 35. Calculate the root mean square speed of hydrogen molecules at 373.15 K. Q 36. Five gas molecules chosen at random are found to have speed of 500, 600, 700, 800 and 900 m/s. Find the rms speed. Is it the same as the average speed? Q 37. The pressure of a gas in a 100 mL container is 200 kPa and the average translational kinetic energy of each gas particle is 6 × 10 21 J. Find the number of gas particles in the container. How many moles are there in the container? Q 38. One gram mole NO2 at 57° C and 2 atm pressure is kept in a vessel. Assuming the molecules to be moving with rms velocity. Find the number of collisions per second which the molecules make with one square meter area of the vessel wall. Q 39. A 2.00 mL volume container contains 50 mg of gas at a pressure of 100 kPa. The mass of each gas particle is 8.0 × 10 26 kg. Find the average translational kinetic energy of each particle. Q 40. Call the rms speed of the molecules in an ideal gas v0 at temperature T0 and pressure p0. Find the speed if (a) the temperature is raised from T0 = 293 K to 573 K (b) the pressure is doubled and T = T0 (c) the molecular weight of each of the gas molecules is tripled. Q 41. At what temperature is the "effective" speed of gaseous hydrogen molecules (molecular weight = 2) equal to that of oxygen molecules (molecular weight = 32) at 47° C? Q 42. At what temperature is vrms of H2 molecules equal to the escape speed from earth's surface. What is the corresponding temperature for escape of hydrogen from moon's surface? Given gm =1.6m/s 2 , Re = 6367 km and Rm =1750 km. Q 43. (a) What is the average translational kinetic energy of a molecule of an ideal gas at temperature of 27° C? (b) What is the total random translational kinetic energy of the molecules in one mole of this gas? (c) What is the rms speed of oxygen molecules at this temperature? Solutions 1. For Q. Nos. 1 and 2 Apply the formula, 3. In the above equation, putting TF = TC, We get Page 5 Exercises For JEE Main Subjective Questions Temperature Scales Q 1. Change each of the given temperatures to the Celsius and Kelvin scales: 68° F, 5° F and 176° F. Q 2. Change each of the given temperatures to the Fahrenheit and Rankine scales: 30° C, 5° C and 20° C. Q 3. At what temperature do the Celsius and Fahrenheit readings have the same numerical value? Q 4. You work in a materials testing lab and your boss tells you to increase the temperature of a sample by 40.0° C The only thermometer you can find at your workbench reads in ° F. If the initial temperature of the sample is 68.2° F. What is its temperature in ° F, when the desired temperature increase has been achieved? Q 5. The steam point and the ice point of a mercury thermometer are marked as 80° and 20°. What will be the temperature in centigrade mercury scale when this thermometer reads 32° ? Thermometers Q 6. The pressure of the gas in a constant volume gas thermometer is 80cm of mercury in melting ice. When the bulb is placed in a liquid, the pressure becomes 160 cm of mercury. Find the temperature of the liquid. Q 7. The resistances of a platinum resistance thermometer at the ice point, the steam point and the boiling point of sulphur are 2.50, 3.50and 6.50 ? respectively. Find the boiling point of sulphur on the platinum scale. The ice point and the steam point measure 0° and 100° respectively. Q 8. In a constant volume gas thermometer, the pressure of the working gas is measured by the difference in the levels of mercury in the two arms of a Utube connected to the gas at one end . When the bulb is placed at the room temperature 27.0° C, the mercury column in the arm open to atmosphere stands 5.00cm above the level of mercury in the other arm. When the bulb is placed in a hot liquid, the difference of mercury levels becomes 45.0cm. Calculate the temperature of the liquid.(Atmospheric pressure = 75.0cm of mercury.) Thermal Expansion (Take values of a from table 17.1) Q 9. An iron ball has a diameter of 6 cm and is 0.010 mm too large to pass through a hole in a brass plate when the ball and plate are at a temperature of 30° C At what temperature, the same for ball and plate, will the ball just pass through the hole ? Q 10. (a) An aluminum measuring rod which is correct at 5° C, measures a certain distance as 88.42cm at 35 ° C. Determine the error in measuring the distance due to the expansion of the rod. (b) If this aluminum rod measures a length of steel as 88.42 cm at 35° C, what is the correct length of the steel at 35° C? Q 11. A steel tape is calibrated at 20° C. On a cold day when the temperature is 15° C, what will be the percentage error in the tape ? Q 12. A steel wire of 2.0 mm 2 crosssection is held straight (but under no tension) by attaching it firmly to two points a distance 1.50mapart at 30 ° C. If the temperature now decreases to 10° C and if the two points remain fixed, what will be the tension in the wire ? For steel, Y = 20,0000 MP a. Q 13. A metallic bob weighs 50 g in air. If it is immersed in a liquid at a temperature of 25° C, it weighs 45 g. When the temperature of the liquid is raised to 100° C, it weighs 45. lg. Calculate the coefficient of cubical expansion of the liquid. Given that coefficient of cubical expansion of the metal is 12 × 10 6 ° C 1 . Gas Laws and ideal Gas Equation Q 14. Find the mass (in kilogram) of an ammonia molecule NH 3. Q 15. An ideal gas exerts a pressure of 1.52 MPa when its temperature is 298.15 K and its volume is 10 2 m 3 . (a) How many moles of gas are there? (b) What is the mass density if the gas is molecular hydrogen? (c) What is the mass density if the gas is oxygen? Q 16. A compressor pumps 70 L of air into a 6 L tank with the temperature remaining unchanged. If all the air is originally at 1 atm. What is the final absolute pressure of the air in the tank? Q 17. A partially inflated balloon contains 500 m 3 of helium at 27° C and 1 atm pressure. What is the volume of the helium at an altitude of 18000 ft, where the pressure is 0.5 atm and the temperature is 3° C? Q 18. A cylinder whose inside diameter is 4.00 cm contains air compressed by a piston of mass m= 13.0 kg which can slide freely in the cylinder. The entire arrangement is immersed in a water bath whose temperature can be controlled. The system is initially in equilibrium at temperature t i =20°C. The initial height of the piston above the bottom of the cylinder is hi = 4.00cm The temperature of the water bath is gradually increased to a final temperature t f = 100° C. Calculate the final height hf of the piston. Q 19. The closed cylinder shown in figure has a freely moving piston separating chambers 1 and 2. Chamber 1 contains 25 mg of N2 gas and chamber 2 contains 40 mg of helium gas. When equilibrium is established what will be the ratio L1 /L2 ? What is the ratio of the number of moles of N2 to the number of moles of He? (Molecular weights of N 2 and He are 28 and 4). Q 20. Two gases occupy two containers A and B. The gas in A of volume 0.11m 3 exerts a pressure of 1.38 MPa. The gas in B of volume 0.16 m 3 exerts a pressure of 0.69 MPa. Two containers are united by a tube of negligible volume and the gases are allowed to intermingle. What is the final pressure in the container if the temperature remains constant ? Q 21. A glass bulb of volume 400cm 3 is connected to another of volume 200cm 3 by means of a tube of negligible volume. The bulbs contain dry air and are both at a common temperature and pressure of 20°C and 1.00 atm. The larger bulb is immersed in steam at 100°C and the smaller in melting ice at 0°C. Find the final common pressure. Q 22. The condition called standard temperature and pressure (STP) for a gas is defined as temperature of 0°C = 273.15K and a pressure of 1 atm = 1.013 × 10 5 Pa. If you want to keep a mole of an ideal gas in your room at STP, how big a container do you need? Q 23. A large cylindrical tank contains 0.750 m 3 of nitrogen gas at 27° C and 1.50 × 10 5 Pa (absolute pressure). The tank has a tightfitting piston that allows the volume to be changed. What will be the pressure if the volume is decreased to 0.480 m 3 and the temperature is increased to 157°C. Q 24. A vessel of volume 5 litres contains 1.4 g of N2 and 0.4 g of He at 1500 K. If 30% of the nitrogen molecules are dissociated into atoms then find the gas pressure. Degree of Freedom, internal Energy and Molar Heat Capacity Q 25. Temperature of diatomic gas is 300 K. If moment of inertia of its molecules is 8.28 × 10 38 gcm 2 . Calculate their root mean square angular velocity. Q 26. How many degrees of freedom have the gas molecules, if under standard conditions the gas density is ? = 1.3 kg/m 3 and velocity of sound propagation on it is v = 330 m/s? Q 27. Three moles of an ideal gas having ? = 1.67 are mixed with 2 moles of another ideal gas having y = 1.4. Find the equivalent value of ? for the mixture. Q 28. If the kinetic energy of the molecules in 5 litres of helium at 2 atm is E. What is the kinetic energy of molecules in 15 litres of oxygen at 3 atm in terms of E ? Q 29. Find the number of degrees of freedom of molecules in a gas. Whose molar heat capacity (a) at constant pressure CP = 29 J mol 1 K 1 (b) C = 29 J mol 1 K 1 in the process PT = constant. Q 30. In a certain gas 2 th 5 of the energy of molecules is associated with the rotation of molecules and the rest of it is associated with the motion of the centre of mass. (a) What is the average translational energy of one such molecule when the temperature is 27°C? (b) How much energy must be supplied to one mole of this gas at constant volume to raise the temperature by 1 °C? Q 31. A mixture contains 1 mole of helium (CP =2.5R, CV =1.5R) and 1 mole of hydrogen (CP =3.5R,CV = 2.5 R). Calculate the values of CP,CV and ? for the mixture. Q 32. Two ideal gases have the same value of C P / CV = ?. What will be the value of this ratio for a mixture of the two such gases in the ratio 1 : 2 ? Q 33. An ideal gas (CP / CV = ?) is taken through a process in which the pressure and the volume vary as P = aV b . Find the value of b for which the specific heat capacity in the process is zero. Q 34. An ideal gas is taken through a process in which the pressure and the volume are changed according to the equation P = kV. Show that the molar heat capacity of the gas for the process is given by C = CV + R 2 Kinetic Theory of Gases Q 35. Calculate the root mean square speed of hydrogen molecules at 373.15 K. Q 36. Five gas molecules chosen at random are found to have speed of 500, 600, 700, 800 and 900 m/s. Find the rms speed. Is it the same as the average speed? Q 37. The pressure of a gas in a 100 mL container is 200 kPa and the average translational kinetic energy of each gas particle is 6 × 10 21 J. Find the number of gas particles in the container. How many moles are there in the container? Q 38. One gram mole NO2 at 57° C and 2 atm pressure is kept in a vessel. Assuming the molecules to be moving with rms velocity. Find the number of collisions per second which the molecules make with one square meter area of the vessel wall. Q 39. A 2.00 mL volume container contains 50 mg of gas at a pressure of 100 kPa. The mass of each gas particle is 8.0 × 10 26 kg. Find the average translational kinetic energy of each particle. Q 40. Call the rms speed of the molecules in an ideal gas v0 at temperature T0 and pressure p0. Find the speed if (a) the temperature is raised from T0 = 293 K to 573 K (b) the pressure is doubled and T = T0 (c) the molecular weight of each of the gas molecules is tripled. Q 41. At what temperature is the "effective" speed of gaseous hydrogen molecules (molecular weight = 2) equal to that of oxygen molecules (molecular weight = 32) at 47° C? Q 42. At what temperature is vrms of H2 molecules equal to the escape speed from earth's surface. What is the corresponding temperature for escape of hydrogen from moon's surface? Given gm =1.6m/s 2 , Re = 6367 km and Rm =1750 km. Q 43. (a) What is the average translational kinetic energy of a molecule of an ideal gas at temperature of 27° C? (b) What is the total random translational kinetic energy of the molecules in one mole of this gas? (c) What is the rms speed of oxygen molecules at this temperature? Solutions 1. For Q. Nos. 1 and 2 Apply the formula, 3. In the above equation, putting TF = TC, We get TF = 40°F or TC = 40°C 4. Initially Finally TC = 20.11+ 40 = 60.11°C 5. 6. At constant volume, 7. 8. At constant volume. = 450K = 450 – 273 = 177°C 9. ? New temperature = (30 + 20.83) = 50.83°C 10. (a) = (88.42) (2.4 × 10 5 ) (35 5) = 0.064 cm (b) At higher temperature it measures less. Hence = (88.42) + (0.064) = 88.484 cm 11. =  (1.2 × 10 5 ) (35) × 100 =  0.042%Read More
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