Explain qualitatively how molecular movement causes the pressure exerted by a gas.
,
.
The calculations in (b) are based on the density for neon being 
. Suggest the effect, if any, on the root-mean-square speed of changing the density at constant temperature.
and pressure 
. For this gas, the product 
is given by the expression
is the mass of a molecule of the gas.
,
.
contains helium-4 gas at pressure 
and temperature 
. Helium-4 may be assumed to be an ideal gas.
is 
of an ideal gas is given by the expression
is the density of the gas.
.
of the atoms of an ideal gas is given by the expression
and contains helium-4 gas at a pressure of 
and at a temperature of 
. Calculate, for the helium gas,
contains 
molecules of an ideal gas. Each molecule has a component 
of velocity normal to one side S of the cube, as shown in the figure below.
of the gas due to the component 
is the mass of a molecule.
is the mean square speed of the molecules.
at a temperature of 
. Calculate the r.m.s. speed of the molecules at a temperature of 
.
may be assumed to be an ideal gas. A mass of 
of argon-40 has a volume of 
at a temperature of 
. Determine, for this mass of argon-40 gas,
may be assumed to be an ideal gas.
.
of an atom of an ideal gas is given by the expression
.
and a temperature of 
, 
of helium gas has a volume of 
. The mass of 
.
.
and volume 
of an ideal gas are related to the density 
of the gas by the expression
.
of a gas molecule is given by
is the Boltzmann constant and 
is the thermodynamic temperature.
of molecules is heated at constant volume. Use the expression in (a)(ii) to show that the thermal energy required to raise the temperature of the gas by 
has a value of 
, where 
is the molar gas constant.
of a molecule of an ideal gas is given by the expression
is the mass of a molecule and 
is the Boltzmann constant. State the meaning of the symbol
contains an ideal gas at pressure 
and temperature 
. The gas is heated. The thermal energy transferred to the gas is 
. The final temperature and pressure of the gas are 
, as illustrated in the figure below.
of molecules in the cylinder,
contains 
molecules of an ideal gas. Each molecule has mass 
. Using the kinetic theory of ideal gases, it can be shown that, if all the molecules are moving with speed 
at right angles to one face of the box, the pressure 
exerted on the face of the box is given by the expression
is the density of the gas and 
is the mean-square speed of the molecules. Explain how each of the following terms in equation 2 is derived from equation 1:
: ...............................................................
. Calculate the mass of one molecule of the gas.
at a pressure of 
and a temperature of 
, as shown in the figure below:
of a molecule of an ideal gas is given by
is the Boltzmann constant and 
is the thermodynamic temperature. Calculate the increase in internal energy 
of the gas during the expansion.
. Use your answer in (i) to explain whether thermal energy is transferred to or from the gas during the expansion.
and volume 
of an ideal gas are related by
is the number of molecules, 
is the mass of a molecule and 
is the mean square speed of the molecules. Use this equation to show that the mean kinetic energy 
of a molecule is given by
is the Boltzmann constant and 
is the thermodynamic temperature.
of oxygen gas at a temperature of 
. The mass of 
of oxygen gas is 
. It may be assumed that the oxygen behaves as an ideal gas. Calculate, for the oxygen gas in the cylinder,
of an ideal gas at pressure of 
and volume 
. The average kinetic energy 
of a molecule of the gas is given by the expression
is the Boltzmann constant and 
is the thermodynamic temperature. The gas is heated at constant pressure so that its temperature rises by 
. Calculate the increase in internal energy of the gas. Explain your working.
of an ideal gas having density 
is given by the expression
.
. The gas has a volume of 
at a pressure 
.
.
. Use the answer in (i) to estimate the actual volume occupied by the gas atoms.
of an ideal gas increases from 
to 
in a large container.
.
. The pressure of the gas is 
and its volume is 
.
of molecules in the gas.
. Determine the root-mean-square (r.m.s.) speed of the gas molecules.
. Calculate the value of the ratio
.
, and a volume of 
at a temperature of 
. The volume of the container is rapidly decreased to 
. The pressure of the helium gas increases to 
and its temperature increases to 
, as illustrated in the figure below.
of a molecule of an ideal gas is given by
is the Boltzmann constant and 
is the thermodynamic temperature. Calculate the change in the total kinetic energy of the molecules of the helium gas.
of a molecule of an ideal gas is given by the expression
is the molar gas constant, 
is the Avogadro constant and 
is the thermodynamic temperature of the gas.
and a proton collide. A nuclear reaction occurs, represented by the equation
. Assuming that a sample of a mixture of deuterium nuclei and protons behaves as an ideal gas, calculate the temperature of the sample for this reaction to occur.
and the volume 
of an ideal gas is given by the expression
is the mass of a gas molecule.
,
.
of a gas molecule at temperature 
is given by the equation
is a constant.
