Page 1 Introductory Exercise 17.2 Q 1. From the graph for an ideal gas state whether m 1 or m 2 is greater? Q 2. A vessel is filled with an ideal gas at a pressure of 20 atm and is at a temperature of 27°C. One half of the mass is removed from the vessel and the temperature of the remaining gas is increased to 87°C. At this temperature find the pressure of the gas. Q 3. A vessel contains a mixture of 7 g of nitrogen and 11 g of carbondioxide at temperature T = 290K. If pressure of the mixture is 1 atm (=1.01 × 10 5 N/m 2 ), calculate its density (R = 8.31 J/molK). Q 4. An electric bulb of volume 250 cm 3 was sealed off during manufacture at a pressure of 10 3 mm of mercury at 27°C. Compute the number of air molecules contained in the bulb. Given that R = 8.31 J/mol K and N A = 6.02 × 10 23 per mol. Q 5. State whether P 1 > P 2 or P 2 > P 1 for given mass of a gas? Q 6. For a given mass of a gas what is the shape of P versus 1 V graph at constant temperature? Solutions 1. At constant volume T P graph is a straight line of slope, Slope of m 1 is less. Hence m 1 is greater. 2. 3. n 1 = number of moles of nitrogen n 2 = number of moles of CO 2 = 4. PV = nRT Page 2 Introductory Exercise 17.2 Q 1. From the graph for an ideal gas state whether m 1 or m 2 is greater? Q 2. A vessel is filled with an ideal gas at a pressure of 20 atm and is at a temperature of 27°C. One half of the mass is removed from the vessel and the temperature of the remaining gas is increased to 87°C. At this temperature find the pressure of the gas. Q 3. A vessel contains a mixture of 7 g of nitrogen and 11 g of carbondioxide at temperature T = 290K. If pressure of the mixture is 1 atm (=1.01 × 10 5 N/m 2 ), calculate its density (R = 8.31 J/molK). Q 4. An electric bulb of volume 250 cm 3 was sealed off during manufacture at a pressure of 10 3 mm of mercury at 27°C. Compute the number of air molecules contained in the bulb. Given that R = 8.31 J/mol K and N A = 6.02 × 10 23 per mol. Q 5. State whether P 1 > P 2 or P 2 > P 1 for given mass of a gas? Q 6. For a given mass of a gas what is the shape of P versus 1 V graph at constant temperature? Solutions 1. At constant volume T P graph is a straight line of slope, Slope of m 1 is less. Hence m 1 is greater. 2. 3. n 1 = number of moles of nitrogen n 2 = number of moles of CO 2 = 4. PV = nRT = 1.33 × 10 8 ? Number of molecular = (n) N A = (1.33 × 10 8 ) (6.02 × 10 23 ) = 8 × 10 15 5. For given mass, VT graph is a straight line passing through origin having Slope of P 2 is more. Hence P 2 < P 1 . 6. i.e., P versus 1 V graph is a straight line passing through origin of slope nRT. Introductory Exercise 17.3 Q 1. The average speed of all the molecules in a gas at a given instant is not zero, whereas the average velocity of all the molecules is zero. Explain why? Q 2. A sample of helium gas is at a temperature of 300 K and a pressure of 0.5 atm. What is the average kinetic energy of a molecule of a gas? Q 3. A sample of helium and neon gases has a temperature of 300 K and pressure of 1.0 atm. The molar mass of helium is 4.0 g/mol and that of neon is 20.2 g/mol. (a) Find the rms speed of the helium atoms and of the neon atoms. (b) What is the average kinetic energy per atom of each gas? Q 4. At what temperature will the particles in a sample of helium gas have an rms speed of 1.0 km/s? Q 5. At 0°C and 1.0 atm (=1.01 × 10 5 N/m 2 ) pressure the densities of air, oxygen and nitrogen are 1.284 kg/m 3 , 1.429 kg/m 3 and 1.251 kg/m 3 respectively. Calculate the percentage of nitrogen in the air from these data, assuming only these two gases to be present. Q 6. An air bubble of 20 cm 3 volume is at the bottom of a lake 40 meters deep where the temperature is 4°C. The bubble rises to the surface which is at a temperature of 20°C. Take the temperature to be the same as that of the surrounding water and find its volume just before it reaches the surface. Q 7. If the water molecules in 1.0 g of water were distributed uniformly over the surface of earth, how many such molecules would there be in 1.0 cm 2 of earth's surface? Q 8. For a certain gas the heat capacity at constant pressure is greater than that at constant volume by 29.1J/K. (a) How many moles of the gas are there? (b) If the gas is monoatomic, what are heat capacities at constant volume and pressure ? Page 3 Introductory Exercise 17.2 Q 1. From the graph for an ideal gas state whether m 1 or m 2 is greater? Q 2. A vessel is filled with an ideal gas at a pressure of 20 atm and is at a temperature of 27°C. One half of the mass is removed from the vessel and the temperature of the remaining gas is increased to 87°C. At this temperature find the pressure of the gas. Q 3. A vessel contains a mixture of 7 g of nitrogen and 11 g of carbondioxide at temperature T = 290K. If pressure of the mixture is 1 atm (=1.01 × 10 5 N/m 2 ), calculate its density (R = 8.31 J/molK). Q 4. An electric bulb of volume 250 cm 3 was sealed off during manufacture at a pressure of 10 3 mm of mercury at 27°C. Compute the number of air molecules contained in the bulb. Given that R = 8.31 J/mol K and N A = 6.02 × 10 23 per mol. Q 5. State whether P 1 > P 2 or P 2 > P 1 for given mass of a gas? Q 6. For a given mass of a gas what is the shape of P versus 1 V graph at constant temperature? Solutions 1. At constant volume T P graph is a straight line of slope, Slope of m 1 is less. Hence m 1 is greater. 2. 3. n 1 = number of moles of nitrogen n 2 = number of moles of CO 2 = 4. PV = nRT = 1.33 × 10 8 ? Number of molecular = (n) N A = (1.33 × 10 8 ) (6.02 × 10 23 ) = 8 × 10 15 5. For given mass, VT graph is a straight line passing through origin having Slope of P 2 is more. Hence P 2 < P 1 . 6. i.e., P versus 1 V graph is a straight line passing through origin of slope nRT. Introductory Exercise 17.3 Q 1. The average speed of all the molecules in a gas at a given instant is not zero, whereas the average velocity of all the molecules is zero. Explain why? Q 2. A sample of helium gas is at a temperature of 300 K and a pressure of 0.5 atm. What is the average kinetic energy of a molecule of a gas? Q 3. A sample of helium and neon gases has a temperature of 300 K and pressure of 1.0 atm. The molar mass of helium is 4.0 g/mol and that of neon is 20.2 g/mol. (a) Find the rms speed of the helium atoms and of the neon atoms. (b) What is the average kinetic energy per atom of each gas? Q 4. At what temperature will the particles in a sample of helium gas have an rms speed of 1.0 km/s? Q 5. At 0°C and 1.0 atm (=1.01 × 10 5 N/m 2 ) pressure the densities of air, oxygen and nitrogen are 1.284 kg/m 3 , 1.429 kg/m 3 and 1.251 kg/m 3 respectively. Calculate the percentage of nitrogen in the air from these data, assuming only these two gases to be present. Q 6. An air bubble of 20 cm 3 volume is at the bottom of a lake 40 meters deep where the temperature is 4°C. The bubble rises to the surface which is at a temperature of 20°C. Take the temperature to be the same as that of the surrounding water and find its volume just before it reaches the surface. Q 7. If the water molecules in 1.0 g of water were distributed uniformly over the surface of earth, how many such molecules would there be in 1.0 cm 2 of earth's surface? Q 8. For a certain gas the heat capacity at constant pressure is greater than that at constant volume by 29.1J/K. (a) How many moles of the gas are there? (b) If the gas is monoatomic, what are heat capacities at constant volume and pressure ? (c) If the gas molecules are diatomic which rotate but do not vibrate, what are heat capacities at constant volume and at constant pressure. Q 9. The heat capacity at constant volume of a sample of a monoatomic gas is 35 J/K. Find : (a) the number of moles (b) the internal energy at 0°C (c) the molor heat capacity at constant pressure. Q 10. For any distribution of speeds v rms ? v av . Is this statement true or false? Solutions 1. See the answer 2. Helium gas is monoatomic. So its degree of freedom f = 3. Average kinetic energy of 1 molecule of gas = 6.21 × 10 21 J 3. (a) For He gas : = 1368 m/s For Ne gas : = 609 m/s (b) Each gas is monotonic for which degree of freedom f = 3. Hence average kinetic energy of one atom = 6.21 × 10 21 J 4. 5. Let mass of nitrogen = (m) g. Then mass of oxygen = (100  m) g. Number of moles of nitrogen, and number of moles of oxygen For air Page 4 Introductory Exercise 17.2 Q 1. From the graph for an ideal gas state whether m 1 or m 2 is greater? Q 2. A vessel is filled with an ideal gas at a pressure of 20 atm and is at a temperature of 27°C. One half of the mass is removed from the vessel and the temperature of the remaining gas is increased to 87°C. At this temperature find the pressure of the gas. Q 3. A vessel contains a mixture of 7 g of nitrogen and 11 g of carbondioxide at temperature T = 290K. If pressure of the mixture is 1 atm (=1.01 × 10 5 N/m 2 ), calculate its density (R = 8.31 J/molK). Q 4. An electric bulb of volume 250 cm 3 was sealed off during manufacture at a pressure of 10 3 mm of mercury at 27°C. Compute the number of air molecules contained in the bulb. Given that R = 8.31 J/mol K and N A = 6.02 × 10 23 per mol. Q 5. State whether P 1 > P 2 or P 2 > P 1 for given mass of a gas? Q 6. For a given mass of a gas what is the shape of P versus 1 V graph at constant temperature? Solutions 1. At constant volume T P graph is a straight line of slope, Slope of m 1 is less. Hence m 1 is greater. 2. 3. n 1 = number of moles of nitrogen n 2 = number of moles of CO 2 = 4. PV = nRT = 1.33 × 10 8 ? Number of molecular = (n) N A = (1.33 × 10 8 ) (6.02 × 10 23 ) = 8 × 10 15 5. For given mass, VT graph is a straight line passing through origin having Slope of P 2 is more. Hence P 2 < P 1 . 6. i.e., P versus 1 V graph is a straight line passing through origin of slope nRT. Introductory Exercise 17.3 Q 1. The average speed of all the molecules in a gas at a given instant is not zero, whereas the average velocity of all the molecules is zero. Explain why? Q 2. A sample of helium gas is at a temperature of 300 K and a pressure of 0.5 atm. What is the average kinetic energy of a molecule of a gas? Q 3. A sample of helium and neon gases has a temperature of 300 K and pressure of 1.0 atm. The molar mass of helium is 4.0 g/mol and that of neon is 20.2 g/mol. (a) Find the rms speed of the helium atoms and of the neon atoms. (b) What is the average kinetic energy per atom of each gas? Q 4. At what temperature will the particles in a sample of helium gas have an rms speed of 1.0 km/s? Q 5. At 0°C and 1.0 atm (=1.01 × 10 5 N/m 2 ) pressure the densities of air, oxygen and nitrogen are 1.284 kg/m 3 , 1.429 kg/m 3 and 1.251 kg/m 3 respectively. Calculate the percentage of nitrogen in the air from these data, assuming only these two gases to be present. Q 6. An air bubble of 20 cm 3 volume is at the bottom of a lake 40 meters deep where the temperature is 4°C. The bubble rises to the surface which is at a temperature of 20°C. Take the temperature to be the same as that of the surrounding water and find its volume just before it reaches the surface. Q 7. If the water molecules in 1.0 g of water were distributed uniformly over the surface of earth, how many such molecules would there be in 1.0 cm 2 of earth's surface? Q 8. For a certain gas the heat capacity at constant pressure is greater than that at constant volume by 29.1J/K. (a) How many moles of the gas are there? (b) If the gas is monoatomic, what are heat capacities at constant volume and pressure ? (c) If the gas molecules are diatomic which rotate but do not vibrate, what are heat capacities at constant volume and at constant pressure. Q 9. The heat capacity at constant volume of a sample of a monoatomic gas is 35 J/K. Find : (a) the number of moles (b) the internal energy at 0°C (c) the molor heat capacity at constant pressure. Q 10. For any distribution of speeds v rms ? v av . Is this statement true or false? Solutions 1. See the answer 2. Helium gas is monoatomic. So its degree of freedom f = 3. Average kinetic energy of 1 molecule of gas = 6.21 × 10 21 J 3. (a) For He gas : = 1368 m/s For Ne gas : = 609 m/s (b) Each gas is monotonic for which degree of freedom f = 3. Hence average kinetic energy of one atom = 6.21 × 10 21 J 4. 5. Let mass of nitrogen = (m) g. Then mass of oxygen = (100  m) g. Number of moles of nitrogen, and number of moles of oxygen For air Solving this equation we get, m = 76.5 g This is also percentage of N 2 by mass on air as total mass we have taken is 100 g. 6. n 1 = n 2 7. Number of gram moles Avogadro number N A = 6.02 × 10 23 /gmol ? Total number of molecules, N =nN A = 3.34 × 10 22 ? Number of molecules per cm 2 8. (a) Molar heat capacity and heat capacity C p = nC P Similarly C V = nC V Now C p  C V = n (C P  C V )  nR (b) = (3.5) (2.5) (8.31)= 72.75 J/K C V = nC V = n = (3.5) (1.5) (8.31)= 43.65 J/K (c) = (3.5) (3.5) (8.31) = 101.8 J/K = (3.5) (2.5) (8.31)= 72.75 J/K 9. (a) As discussed in the above problem. C V = nC V (b) Internal energy Page 5 Introductory Exercise 17.2 Q 1. From the graph for an ideal gas state whether m 1 or m 2 is greater? Q 2. A vessel is filled with an ideal gas at a pressure of 20 atm and is at a temperature of 27°C. One half of the mass is removed from the vessel and the temperature of the remaining gas is increased to 87°C. At this temperature find the pressure of the gas. Q 3. A vessel contains a mixture of 7 g of nitrogen and 11 g of carbondioxide at temperature T = 290K. If pressure of the mixture is 1 atm (=1.01 × 10 5 N/m 2 ), calculate its density (R = 8.31 J/molK). Q 4. An electric bulb of volume 250 cm 3 was sealed off during manufacture at a pressure of 10 3 mm of mercury at 27°C. Compute the number of air molecules contained in the bulb. Given that R = 8.31 J/mol K and N A = 6.02 × 10 23 per mol. Q 5. State whether P 1 > P 2 or P 2 > P 1 for given mass of a gas? Q 6. For a given mass of a gas what is the shape of P versus 1 V graph at constant temperature? Solutions 1. At constant volume T P graph is a straight line of slope, Slope of m 1 is less. Hence m 1 is greater. 2. 3. n 1 = number of moles of nitrogen n 2 = number of moles of CO 2 = 4. PV = nRT = 1.33 × 10 8 ? Number of molecular = (n) N A = (1.33 × 10 8 ) (6.02 × 10 23 ) = 8 × 10 15 5. For given mass, VT graph is a straight line passing through origin having Slope of P 2 is more. Hence P 2 < P 1 . 6. i.e., P versus 1 V graph is a straight line passing through origin of slope nRT. Introductory Exercise 17.3 Q 1. The average speed of all the molecules in a gas at a given instant is not zero, whereas the average velocity of all the molecules is zero. Explain why? Q 2. A sample of helium gas is at a temperature of 300 K and a pressure of 0.5 atm. What is the average kinetic energy of a molecule of a gas? Q 3. A sample of helium and neon gases has a temperature of 300 K and pressure of 1.0 atm. The molar mass of helium is 4.0 g/mol and that of neon is 20.2 g/mol. (a) Find the rms speed of the helium atoms and of the neon atoms. (b) What is the average kinetic energy per atom of each gas? Q 4. At what temperature will the particles in a sample of helium gas have an rms speed of 1.0 km/s? Q 5. At 0°C and 1.0 atm (=1.01 × 10 5 N/m 2 ) pressure the densities of air, oxygen and nitrogen are 1.284 kg/m 3 , 1.429 kg/m 3 and 1.251 kg/m 3 respectively. Calculate the percentage of nitrogen in the air from these data, assuming only these two gases to be present. Q 6. An air bubble of 20 cm 3 volume is at the bottom of a lake 40 meters deep where the temperature is 4°C. The bubble rises to the surface which is at a temperature of 20°C. Take the temperature to be the same as that of the surrounding water and find its volume just before it reaches the surface. Q 7. If the water molecules in 1.0 g of water were distributed uniformly over the surface of earth, how many such molecules would there be in 1.0 cm 2 of earth's surface? Q 8. For a certain gas the heat capacity at constant pressure is greater than that at constant volume by 29.1J/K. (a) How many moles of the gas are there? (b) If the gas is monoatomic, what are heat capacities at constant volume and pressure ? (c) If the gas molecules are diatomic which rotate but do not vibrate, what are heat capacities at constant volume and at constant pressure. Q 9. The heat capacity at constant volume of a sample of a monoatomic gas is 35 J/K. Find : (a) the number of moles (b) the internal energy at 0°C (c) the molor heat capacity at constant pressure. Q 10. For any distribution of speeds v rms ? v av . Is this statement true or false? Solutions 1. See the answer 2. Helium gas is monoatomic. So its degree of freedom f = 3. Average kinetic energy of 1 molecule of gas = 6.21 × 10 21 J 3. (a) For He gas : = 1368 m/s For Ne gas : = 609 m/s (b) Each gas is monotonic for which degree of freedom f = 3. Hence average kinetic energy of one atom = 6.21 × 10 21 J 4. 5. Let mass of nitrogen = (m) g. Then mass of oxygen = (100  m) g. Number of moles of nitrogen, and number of moles of oxygen For air Solving this equation we get, m = 76.5 g This is also percentage of N 2 by mass on air as total mass we have taken is 100 g. 6. n 1 = n 2 7. Number of gram moles Avogadro number N A = 6.02 × 10 23 /gmol ? Total number of molecules, N =nN A = 3.34 × 10 22 ? Number of molecules per cm 2 8. (a) Molar heat capacity and heat capacity C p = nC P Similarly C V = nC V Now C p  C V = n (C P  C V )  nR (b) = (3.5) (2.5) (8.31)= 72.75 J/K C V = nC V = n = (3.5) (1.5) (8.31)= 43.65 J/K (c) = (3.5) (3.5) (8.31) = 101.8 J/K = (3.5) (2.5) (8.31)= 72.75 J/K 9. (a) As discussed in the above problem. C V = nC V (b) Internal energy f = degree of freedom = 3 (c) 10. Suppose n 1 molecules have v 1 velocity and n 2 molecules have v 2 velocity. Then Now, v rms ? V av because v 1 and v 2 may be in opposite direction also.Read More
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