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15. Ideal gases
A section of Physics, 9702
Listing 10 of 88 questions
A large container of volume 85 m3 is filled with 110 kg of an ideal gas. The pressure of the gas is 1.0 × 105 Pa at temperature T. The mass of 1.0 mol of the gas is 32 g. Show that the temperature T of the gas is approximately 300 K. The temperature of the gas is increased to 350 K at constant volume. The specific heat capacity of the gas for this change is 0.66 J kg−1 K−1. Calculate the energy supplied to the gas by heating. energy = J Explain how movement of the gas molecules causes pressure in the container. The temperature of a gas depends on the root-mean-square (r.m.s.) speed of its molecules. Calculate the ratio: r.m.s. speed of gas molecules at 350 K r.m.s. speed of gas molecules at 300 K . ratio =
9702_m20_qp_42
THEORY
2020
Paper 4, Variant 2
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A fixed mass of an ideal gas is at a temperature of 21 °C. The pressure of the gas is 2.3 × 105 Pa and its volume is 3.5 × 10–3 m3. Calculate the number N of molecules in the gas. N = The mass of one molecule of the gas is 40 u. Determine the root-mean-square (r.m.s.) speed of the gas molecules. r.m.s. speed = m s–1 The temperature of the gas is increased by 84 °C. Calculate the value of the ratio new r.m.s. speed of molecules original r.m.s. speed of molecules . ratio =
9702_m21_qp_42
THEORY
2021
Paper 4, Variant 2
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State what is meant by an ideal gas. A fixed amount of helium gas is sealed in a container. The helium gas has a pressure of 1.10 × 105 Pa, and a volume of 540 cm3 at a temperature of 27 °C. The volume of the container is rapidly decreased to 30.0 cm3. The pressure of the helium gas increases to 6.70 × 106 Pa and its temperature increases to 742 °C, as illustrated in . initial state final state No thermal energy enters or leaves the helium gas during this process. Show that the helium gas behaves as an ideal gas. The first law of thermodynamics may be expressed as ΔU = q + W. Use the first law of thermodynamics to explain why the temperature of the helium gas increases. 1.10 × 105 Pa 540 cm3 27 °C 6.70 × 106 Pa 30.0 cm3 742 °C The average translational kinetic energy EK of a molecule of an ideal gas is given by EK = 3 2 kT where k is the Boltzmann constant and T is the thermodynamic temperature. Calculate the change in the total kinetic energy of the molecules of the helium gas. change in kinetic energy = J The mass of nitrogen gas in another container is 24.0 g at a temperature of 27 °C. The gas is cooled to its boiling point of –196 °C. Assume all the gas condenses to a liquid. For this change the specific heat capacity of nitrogen gas is 1.04 kJ kg–1 K–1. The specific latent heat of vaporisation of nitrogen is 199 kJ kg–1. Determine the thermal energy, in kJ, removed from the nitrogen gas. energy = kJ
9702_m23_qp_42
THEORY
2023
Paper 4, Variant 2
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State what is meant by an ideal gas. The product of pressure p and volume V of an ideal gas of density ρ at temperature T is given by the expressions and where N is the number of molecules and k is the Boltzmann constant. State the meaning of the symbol . Deduce that the mean kinetic energy EK of the molecules of an ideal gas is given by the expression EK =  kT. In order for an atom to escape completely from the Earth’s gravitational field, it must have a speed of approximately 1.1 × 104m s–1 at the top of the Earth’s atmosphere. Estimate the temperature at the top of the atmosphere such that helium, assumed to be an ideal gas, could escape from the Earth. The mass of a helium atom is 6.6 × 10–27kg. temperature = K Suggest why some helium atoms will escape at temperatures below that calculated in . p =  ρ pV = NkT, Use
9702_s05_qp_4
THEORY
2005
Paper 4, Variant 0
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Some gas, initially at a temperature of 27.2 °C, is heated so that its temperature rises to 38.8 °C. Calculate, in kelvin, to an appropriate number of decimal places, the initial temperature of the gas, initial temperature = K the rise in temperature. rise in temperature = K The pressure p of an ideal gas is given by the expression p = 1 3ρc 2 where ρ is the density of the gas. State the meaning of the symbol c 2. Use the expression to show that the mean kinetic energy of the atoms of an ideal gas is given by the expression = 3 2 kT. Explain any symbols that you use. Helium-4 may be assumed to behave as an ideal gas. A cylinder has a constant volume of 7.8 × 103 cm3 and contains helium-4 gas at a pressure of 2.1 × 107 Pa and at a temperature of 290 K. Calculate, for the helium gas, the amount of gas, amount = mol the mean kinetic energy of the atoms, mean kinetic energy = J the total internal energy. internal energy = J
9702_s10_qp_41
THEORY
2010
Paper 4, Variant 1
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State what is meant by an ideal gas. Two cylinders A and B are connected by a tube of negligible volume, as shown in . tap T tube cylinder A cylinder B 2.5 × 103 cm3 1.6 × 103 cm3 4.9 × 105 Pa 3.4 × 105 Pa 300 K Initially, tap T is closed. The cylinders contain an ideal gas at different pressures. Cylinder A has a constant volume of 2.5 × 103 cm3 and contains gas at pressure 3.4 × 105 Pa and temperature 300 K. Show that cylinder A contains 0.34 mol of gas. Cylinder B has a constant volume of 1.6 × 103 cm3 and contains 0.20 mol of gas. When tap T is opened, the pressure of the gas in both cylinders is 3.9 × 105 Pa. No thermal energy enters or leaves the gas. Determine the final temperature of the gas. temperature = K By reference to work done and change in internal energy, suggest why the temperature of the gas in cylinder A has changed.
9702_s13_qp_41
THEORY
2013
Paper 4, Variant 1
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State what is meant by an ideal gas. Two cylinders A and B are connected by a tube of negligible volume, as shown in . tap T tube cylinder A cylinder B 2.5 × 103 cm3 1.6 × 103 cm3 4.9 × 105 Pa 3.4 × 105 Pa 300 K Initially, tap T is closed. The cylinders contain an ideal gas at different pressures. Cylinder A has a constant volume of 2.5 × 103 cm3 and contains gas at pressure 3.4 × 105 Pa and temperature 300 K. Show that cylinder A contains 0.34 mol of gas. Cylinder B has a constant volume of 1.6 × 103 cm3 and contains 0.20 mol of gas. When tap T is opened, the pressure of the gas in both cylinders is 3.9 × 105 Pa. No thermal energy enters or leaves the gas. Determine the final temperature of the gas. temperature = K By reference to work done and change in internal energy, suggest why the temperature of the gas in cylinder A has changed.
9702_s13_qp_43
THEORY
2013
Paper 4, Variant 3
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Questions Discovered
88