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15.2. Equation of state
A subsection of Physics, 9702, through 15. Ideal gases
Listing 10 of 19 questions
State two of the basic assumptions of the kinetic theory of gases. An ideal gas has amount of substance n. The gas is initially in state X, with pressure 2p and volume V. The gas is cooled at constant volume to state Y, with pressure p. The gas is then heated at constant pressure to state Z, with volume 2V. Finally, the gas returns at constant temperature to state X. Determine an expression for the temperature T of the gas in state X, in terms of n, p and V. Identify any other symbols that you use. On , sketch the variation with volume of pressure for the gas as the gas undergoes the three changes. The state X is labelled. Label states Y and Z. pressure volume V 2V p 2p X During the change of state from Y to Z, the increase in internal energy of the gas is U. During the change of state from Z to X, the work done on the gas is W. Complete Table 4.1 to indicate, for each of the three changes of state, the increase in internal energy of the gas, the thermal energy transferred to the gas and the work done on the gas, in terms of p, V, U and W. Table 4.1 change increase in internal energy of gas thermal energy transferred to gas work done on gas X to Y Y to Z +U Z to X +W
9702_s23_qp_43
THEORY
2023
Paper 4, Variant 3
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The product of the pressure p and the volume V of an ideal gas is given by the expression pV = 1 3Nm where m is the mass of one molecule of the gas. State the meaning of the symbol N, . The product pV is also given by the expression pV = NkT. Deduce an expression, in terms of the Boltzmann constant k and the thermodynamic temperature T, for the mean kinetic energy of a molecule of the ideal gas. A cylinder contains 1.0 mol of an ideal gas. The volume of the cylinder is constant. Calculate the energy required to raise the temperature of the gas by 1.0 kelvin. energy = J The volume of the cylinder is now allowed to increase so that the gas remains at constant pressure when it is heated. Explain whether the energy required to raise the temperature of the gas by 1.0 kelvin is now different from your answer in .
9702_w13_qp_41
THEORY
2013
Paper 4, Variant 1
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The product of the pressure p and the volume V of an ideal gas is given by the expression pV = 1 3Nm where m is the mass of one molecule of the gas. State the meaning of the symbol N, . The product pV is also given by the expression pV = NkT. Deduce an expression, in terms of the Boltzmann constant k and the thermodynamic temperature T, for the mean kinetic energy of a molecule of the ideal gas. A cylinder contains 1.0 mol of an ideal gas. The volume of the cylinder is constant. Calculate the energy required to raise the temperature of the gas by 1.0 kelvin. energy = J The volume of the cylinder is now allowed to increase so that the gas remains at constant pressure when it is heated. Explain whether the energy required to raise the temperature of the gas by 1.0 kelvin is now different from your answer in .
9702_w13_qp_42
THEORY
2013
Paper 4, Variant 2
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State what is meant by an ideal gas. A storage cylinder for an ideal gas has a volume of 3.0 × 10−4 m3. The gas is at a temperature of 23 °C and a pressure of 5.0 × 107 Pa. Show that the amount of gas in the cylinder is 6.1 mol. The gas leaks slowly from the cylinder so that, after a time of 35 days, the pressure has reduced by 0.40%. The temperature remains constant. Calculate the average rate, in atoms per second, at which gas atoms escape from the cylinder. rate = s−1
9702_w14_qp_41
THEORY
2014
Paper 4, Variant 1
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State what is meant by an ideal gas. A storage cylinder for an ideal gas has a volume of 3.0 × 10−4 m3. The gas is at a temperature of 23 °C and a pressure of 5.0 × 107 Pa. Show that the amount of gas in the cylinder is 6.1 mol. The gas leaks slowly from the cylinder so that, after a time of 35 days, the pressure has reduced by 0.40%. The temperature remains constant. Calculate the average rate, in atoms per second, at which gas atoms escape from the cylinder. rate = s−1
9702_w14_qp_42
THEORY
2014
Paper 4, Variant 2
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The equation of state for an ideal gas of volume V at pressure p is pV = nRT where R is the molar gas constant. State what is meant by the symbol n, the symbol T. An ideal gas is held in a container of volume 2.4 × 103 cm3 at pressure 4.9 × 105 Pa. The temperature of the gas is 100 °C. Show that the number of molecules of the gas in the container is 2.3 × 1023. Use data from to estimate the mean distance between molecules in the gas. mean distance = cm
9702_w16_qp_42
THEORY
2016
Paper 4, Variant 2
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State what is meant by an ideal gas. An ideal gas comprised of single atoms is contained in a cylinder and has a volume of 1.84 × 10–2 m3 at a pressure of 2.12 × 107 Pa. The mass of gas in the cylinder is 3.20 kg. Determine, to three significant figures, the root-mean-square (r.m.s.) speed of the atoms of the gas. r.m.s. speed = m s–1 The temperature of the gas in the cylinder is 22 °C. Determine, to three significant figures, 1. the amount, in mol, of the gas, amount = mol 2. the mass of one atom of the gas. mass = kg Use your answer in part 2 to determine the nucleon number A of an atom of the gas. A =
9702_w18_qp_42
THEORY
2018
Paper 4, Variant 2
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Questions Discovered
19